If we accept what Odin told Loki in Thor: The Dark World, then none of the Asgardians in the MCU are genuine gods.
LOKI: I went down to Midgard to rule the people of Earth as a benevolent god. Just like you.
ODIN: We are not gods. We are born, we live, we die. Just as humans do.
LOKI: Give or take 5000 years.
Thor: The Dark World (2013)
Some of the dialogue in the first Thor film implies that Asgardians are just advanced aliens who were perceived as gods by primitive humans.
JANE FOSTER: But you're the one who's always pushing me to chase down every possibility, every alternative!
ERIK SELVIG: I'm talking about science, not magic!
JANE FOSTER: Well, magic's just science that we don't understand yet. Arthur C. Clarke.
ERIK SELVIG: Who wrote science fiction.
JANE FOSTER: A precursor to science fact!
ERIK SELVIG: In some cases, yeah.
JANE FOSTER: Well, if there is an Einstein-Rosen Bridge, then there's something on the other side. And advanced beings could have crossed it!
ERIK SELVIG: But, Jane...
DARCY LEWIS: A primitive culture like the Vikings might have worshipped them as deities.
JANE FOSTER: Yes! Yes, exactly. Thank you.
This was reiterated in Agents of S.H.I.E.L.D., where Asgardians were explicitly referred to as "aliens".
SKYE: So, Asgardians are aliens from another planet that visited us thousands of years ago?
AGENT COULSON: Or more.
SKYE: And because we couldn't understand aliens, we thought they were gods? They pass by May, testing an artifact on the floor.
AGENT COULSON: That's where our Norse mythology comes from.
SKYE: [sighs] That's too crazy. Do you think other deities are aliens, too? Vishnu for sure, right?
Agents of S.H.I.E.L.D. - S01E08 - "The Well"
Also, the tech used by the Asgardians and Dark Elves in Thor: The Dark World -- such as the spaceships, gun turrets, black hole grenades, and the force-field the Asgardians attempted to raise around their palace -- looks more sci-fi than fantasy, and the Bifrost appears to be a glorified Stargate, opening wormholes between points in space.
Regardless of whether you view Asgardians as gods or aliens, I don't see any apparent distinction made between individual Asgardians in that regard.
Some distinctions clearly do exist within Asgardian society, but those appear to be equivalent to the ones which exist within many
human societies: i.e. you have a royal family, the military, and the regular civilians.
In regard to relative strength levels, Thor appears substantially
stronger than all other Asgardians, with the exception of Hela, and possibly Odin. So if you're asking whether the average Asgardian is anywhere near as strong as Thor, the answer is a definite "no".
However, while Sif and the Warriors Three (Hogun, Fandral, and Volstagg) don't seem nearly as strong as Thor, they are nonetheless very clearly superhuman in their own right. In the clip below, from the Agents of S.H.I.E.L.D. episode, "Yes Men", Sif sends an RV sliding several metres along a road by shoving it with one foot.
And as Geneworm pointed out in the comments, there was another Agents of S.H.I.E.L.D. episode, "The Well", where Agent Ward thrust a knife towards an Asgardian going by the name of "Elliot Randolph", and Randolph was able to catch the blade and crumple it in his bare hand, with no visible pain or injury.
According to Randolph, he came to Earth as a member of the Berserker Army, but prior to that, he'd been a mason for thousands of years. After deciding to remain on Earth when the rest of the Berserker Army returned to Asgard, he made a life for himself as a history professor.
AGENT COULSON: Do you know Thor?
ELLIOT RANDOLPH: Oh, sure, I spent all my days palling around with the future King of Asgard. No, I don't know Thor. I was a mason. I broke rocks. Mmmhmm. [chuckling] For thousands of years. If you can imagine that. So when they came, asking for people to fight, yes, of course I signed up. I think, really, I just wanted to travel.
Agents of S.H.I.E.L.D. - S01E08 - "The Well"
Randolph was later stabbed in the chest by a section of an Asgardian staff wielded by a human temporarily endowed with super-strength, so he wasn't invulnerable, but a regular knife wielded by a normal human apparently wasn't up to the job.
Most other 'civilian' type Asgardians haven't been shown in action, and presumably have inferior physical conditioning to warriors like Sif. But I see no reason to think they're weaker than the warriors to a greater extent than human civilians are weaker than human warriors.
This is made very clear in respect to the comics, since the Official Handbooks specify that eldery Asgardian women (such as Frigga) can lift 20 tons, average women (such as Amora), 25, average men (such as Fandral), 30, above-average women (such as Sif), 30, and above-average men (such as Heimdall, Hogun, and Volstagg), 35.
Thor & Hercules: Encyclopaedia Mythologica