It would be terribly harsh to stereotype entire races / empires in the Star Trek universe to entire real world groups of people. As you mention there are certain parallels such as the Klingon Empire to the Soviet Union. At least during the TOS era this seems to hold up; especially considering the link between Praxis and a certain nuclear disaster. See "background information."
That being said I always tend to imagine the species and societies that appear in Star Trek to be analogies of human qualities. Most often enemies of the protagonists seem to demonstrate negative qualities that we see in ourselves and our current world. Qualities we wish to overcome. Other times groups in Star Trek demonstrate positive qualities that we wish to strive for.
"A Ferengi without profit is no Ferengi at all." -Rule of Acquisition #18
The Ferengi live and breath capitalism to the extreme. Without delving into the merits of economic systems: the kind of capitalism that the Ferengi practice is oppressive and corrupt. Labor laws are nearly non existent, bribery is rampant, quasi-slavery (in the form of oppressed females), and price gouging are the ways of the Ferengi. If you were dying of thirst you better damn well make sure you have latinum on you! The Ferengi represent the worst that greed can bring out in people. They are often concerned more with personal wealth than the well-being of society as a whole.
Who could they represent?
There are clear links to the Ferengi and bosses during the Industrial Revolution. In fact the DS9 episode "Bar Association" deals with employees of Quark's bar attempting to form a labor union. Miles O'Brien actually draws a parallel to their endeavor and a (nearly factual) event that took place on Earth: the Anthracite strike of 1902. All this being said, the Ferengi represent anyone who puts personal wealth first to the exclusion of all others. People that price gouge food, water, and medicine during a hurricane, people that find a loop hole in a worker's comp agreement to avoid paying an injured worker, people that exploit sweatshops... They are all the Ferengi.
Klingons: War Mongering / Honor / Hypocrisy
Woah! That's a lot. Of course they represent a lot, they've existed since TOS and are a staple of the franchise. The Klingons were a recurring villain in TOS, hence they needed to be mean and angry. They like their fighting, no doubt about that. They exalt personal strength as well as strength of the empire itself. They are quick to anger and prefer to solve their problems with a Bat'leth or a D7 Battle Cruiser. In fact their society is rooted in fighting
as leadership of the Klingon High Council could be won by a duel to
the death. See "Dominion War."
Yet they are honorable. Worf, being the most prolific Klingon we see on screen gives us countless examples of his personal honor. The empire displays its love for honor during the Khitomer Massacre (possible spoilers in that link). The Romulans (we'll get to them next) launch a sneak attack on the Klingon's Khitomer outpost. A general distress signal is sent and out and the U.S.S Enterprise C a warship of a hated enemy comes to their aid. Not only that, the Enterprise C stands with them and is lost
or WAS IT?
protecting the Klingon colony from the treacherous Romulans. The Klingons are so impressed with the act of bravery portrayed by the hated Federation that they sign the Khitomer Accords and peace ensues.
Klingons often consider honor a matter of life and death. You can't shake hands with a Klingon without him or her mentioning how you insulted their honor. Watch as they pull a knife on you to redeem themselves in the eyes of their house!
All that honor talk makes your head spin. It gets worse when you realize that sometimes it's just that: talk. Remember the Khitomer Massacre? Well as it turns out
Mogh (father of Worf) was branded as a traitor because he apparently
gave precious intelligence to the Romulans allowing them to lower
planetary defenses and leave the colony at Khitomer ripe for attack.
This of course is not true, it turns out that a member of the House
of Duras was the actual traitor! What's more is that the
Chancellor at the time knew about this but because the House of
Duras was so powerful he covered it up in order to avoid a Klingon
Pfft! Talk about "honor." Whether or not this was for the greater good, it still demonstrates hypocrisy of the highest order. When push comes to shove some Klingons will forget their honor.
Who could they represent?
The Norse! Klingon heaven is called "Stovokor." How do you get there? By dying as a warrior of course! Valhalla here we come.
Vikings / Samurai! If Vikings and Samurai (or what Western writers think of them) had a baby you'd get Klingons. Emphasis on a personal code of honor comes from the Samurai. Emphasis on bar brawls and warring comes from the Vikings.
Soviet Union! The question brings this link up. This is true of the TOS era when the Klingons were representative of the looming threat the cold war posed. As time went on Klingon portrayal changes as this wikipedia article notes.
The TNG Klingons are just a conglomeration of any "honorable warrior" stereotype you can think of from real life.
Romulans: Xenophobia / Treachery / Social Oppression
The Romulans were xenophobes. According to the memory alpha page on xenophobia this is expressed in episodes ENTERPRISE: "Future Tense"; TOS: "The Tholian Web." Between TOS and TNG they had developed a neutral zone with the Federation and no one had had contact with them for several decades.
The Romulans were treacherous conniving backstabbers. They plotted and schemed to gain an advantage. I hate beating a dead Klingon but the Khitomer Massacre once again serves as a great example for us.
The Romulans lowered planetary defenses and bombarded population
centers with an expected 78% casualty rate. This bombardment did not
discriminate from civilians! How treacherous.
Let's also not forget their intelligence service: the Tal Shiar. This intelligence service excels at subterfuge of the enemy along with keeping its own people in line. Romulan people feared the Tal Shiar nearly as much as the Empire's enemies.
The covert, often invisible presence of the Tal Shiar kept the general
populace in a constant state of paranoia. Dissent and dissatisfaction
with the status quo were met with severe punishment and often
dissidents have been known to "disappear".
Who could they represent?
The Tal Shiar certainly exemplifies some of the worst characteristics of real world intelligence / secret police agencies. The KGB was known for making dissidents "disappear."
You can't mention Romulans without mentioning the Romans. I personally don't give much credit that they were "based" on the Romans so much as the titles and government structure fit neatly in with "evil empire." Though after reading this wikipedia article you may have a different opinion on the matter.
Any nation or group of people that ever wanted to ignore the outside world by shutting their borders or not interfering with world affairs at large. Perhaps ancient china or pre-WWII Isolationist Americans?
Jem'Hadar: Drug Addiction / Indoctrination / Blind Faith
The question specifically asks about the Jem'Hadar. These people were engineered to be addicted to a drug. They were subsequently controlled by the distribution of said drug. They worshiped the Founders as gods because that's what they were told from birth. They never sought to question whether or not they should. Even if they had it probably wouldn't have done any good. They would have been deprived of their ketracel-white and died shortly after expressing doubt in the Founders.
Who could they represent?
This is tricky. There really isn't one group or example I can point to for them. North Korea comes to mind. They worship their leader as a living god much like the Jem'Hadar worship the Founders. The people of North Korea are "addicted" to what their leader provides. I'm reaching here, but the Jem'Hadar could be representative of any real world cult of personality.
United Federation Of Planets: Social Enlightenment / Peace Loving / Technological Advancement
That's right, the good guys. The United Federation of Planets represents all that is right in the world, all that could be right, all that should be right. (Except when there needs to be drama, because it IS a TV show after all.) Greed? Nope. Fighting over territory and resources? Nope. Anyone go hungry? Not on Earth at least! Anyone getting shot or murdered in the street? Not on Earth at least! People volunteer for Starfleet not for money, but for exploration and peace keeping. And as Picard so aptly put it in Star Trek: First Contact: "We work to better ourselves and the rest of humanity."
Who could they represent?
In the TOS era they most likely represented the US and Western Allies united against the common threat of the Soviet Union.
It goes beyond that though. The Federation represents what the world could be if we strive to make it a better place. If we throw away our negative qualities and focus on the good in each other and ourselves we can achieve great things, even very nearly paradise.
Citizens of the United Federation of Planets are represented in philanthropists, volunteers, charities, social equality advocates, educators, and selflessness. In short: the best qualities we see in ourselves.
Were writers influenced by real world people or groups when devising cultures on Star Trek? Of course they were. It would be impossible for a writer to imagine a Humanoid species and not draw on what they know of the only Humanoid species they have access to: us. Did the writers sit down and draw up a chart and say: "okay guys, the Romulans are Romans with a hint of Soviet Union. The Cardassians are Space Nazis. The Klingons are the Soviet Union but THEN they turn into Samurai Vikings..." No. I cannot imagine they did. Any parallels you or I see in the cultures on Star Trek stem in most cases from subtle borrowings from what the writers on Trek knew.