Is it just a coincidence he speaks both Chewie and Greedo? Chewie, sure, he's had all the time in the world to learn. But Greedo's kind of an asshole. Not the kind of dude whose conversational delights are going to tempt anyone to bear down and learn a new language for the pleasure of participation. And: Han speaks Jabba, too? Jabba's clearly not speaking Greedo. True, in his own lines he's speaking human to them, but he clearly understands everything they're jibber-jabbering back at him.
Is Solo some kind of specialist in the languages of Tatooine (with a side of wookie for business and good-buddy purposes), or does he speak a comparable selection of local languages at each of the shithole planets he puts the Falcon into port at? We don't get the impression Solo lives in Tatooine. He's just soaking in the wretched atmosphere of scum and villainy at Mos Eisely, keeping an eye out for an easy score, meanwhile enjoying the jazz scene. He's not there to make a thorough study of tongues.
I'm not saying it's impossible for him to have mastered a few languages. I'm just saying it raises an eyebrow. It's a little convenient. Han's not the type you expect to put all that effort and study in, just to impress a few of these fringe species types with his thoughtful grasp of their beloved mother tongue. Especially given he can't be bothered to answer back in it.
The fact these different folks all understand Han doesn't seem too problematic to me. Realistically, everybody pretty much has to understand English. It's clearly the official State Language. These monocultural and definitely English-speaking Imperials who've been ruling this galaxy with an iron fist aren't going to foster some multi-culti polyglot paradise! That Trooper asks you a question, you better be hip to his jive talk. And I suspect if you can't answer in him back in something he can understand, you may find yourself up shit creek in Dagoba without a Gronkneik.
The more you examine it, the more peculiar Han Solo's love of languages seems. I wish we'd learned a bit more about this guy's backstory.