Despite the fact that Han Solo and Dr. Jones look eerily similar, did the Star Wars saga occur in Jones' galaxy (and thus Jones not being in our own)? The question stems from a few references in Jones' world: The hieroglyphics in Raiders showing C-3PO and R2D2 and the bar in Temple named Club Obi-Wan.
Indy has far too many references to Earth specific events and objects to be a coincidence. The World Wars, The Ark of the Covenant, Nazis, Harvard University, Venice, planes, automobiles, trains, rifles, pistols, swords, whips...
The maps in the movie also show pretty clearly that they are on earth. The maps are quite iconic although I can't seem to find a sample image at the moment.
For another planet in another galaxy to have a planet with the same layout of continents, with the same countries with the same cities with the same names, with the same technology and the same universities and the same religions...it's all a bit much.
As for the references to star wars characters, it is either a coincidence and we are mistaking the hieroglyphs for looking like those characters when they are something else, such as a guy in a type of armor and some kind of false idol/utility -- or those characters (or similar models) somehow made it to visit the ancient civilizations that made those hieroglyphs, through an adventure we have not yet seen.
Yes, they are in the same Universe (though, as others noted, not in the same galaxy).
It was already established that E.T. (which takes place on real Earth) and Star Wars are in the same Universe.
Since it seems fairly obvious that E.T. Earth is the same one as Indy Earth, they are both in the Star Wars Universe.
However, the specific hieroglyphs are, indeed, likely unrelated. There are plenty of ancient drawings that are interpreted as all sorts of paleo contacts, if one tries to look at them from weird enough angles.
Depending on how credible you find the comic books, the answer is yes. In Star Wars Tales #19:
In this short story, Han and Chewie are on the run from the Imperial fleet and, as a desperation move, force the Millennium Falcon to complete a blind hyperspace jump. The jump deposits them in our solar system (which Han doesn't recognize), and the Falcon crash lands in the American Northwest. Han comments on its resemblance to Endor, and the two smugglers set out to find a settlement. A Native American tribe sees the duo and riddles Han with a flurry of arrows. After Chewbacca butchers Han's assailants, Han dies, leaving the Wookiee on Earth all by his lonesome.
Then, this happens...
The story was called "Into the Great Unknown".
If Star Wars was "a long time go in a galaxy far away" it just means that the evens of the trilogy's are happening 4 to 5000 years ago, and that at some point in their adventures, the droids end up out of their galaxy, and are recorded has hieroglyphs! It also means if Han Solo was around for the adventure and had a little fun Captain Kirk style while on earth, of course he could be Indy's many great grandfather! In fact, Earth could have been a lost human colony of the human-like races from Star Wars!