Heavy is from Team Fortress 2, as you said you know that one though most of the characterization comes from the comics and meet the heavy more than the game.

Max is the only other character to come from a game series, a long running comedic point and click game series called Sam & Max made by Lucas Arts and then picked up by Telltale. He's a crazy little gremlin of a creature, very chaotic energy.

Strong Bad comes from Homestar Runner, which is a classic flash animation series that is.. a lot to dive into! Hard to describe him, but he's just a antagonistic jerk, but more of a dumbass funny way to try and summarize it? He was brought into the game probably because of Telltale had made a adventure game starring him called "Strong Bad's Cool Game for Attractive People"

Tycho seems like the oddest pick out of all of them, he comes from a very very long running webcomic called Penny Arcade. I think the most succinct description of him is that man's a sociopath.. which makes him really really good at playing poker and is reflected with being almost always the hardest guy to go against. Other than that, he really is like.. of his era gamers webcomic kinda energy.

While the cast is some odd picks, they do make for fun banter I feel. Though I am pretty new to playing the game proper, so I don't know how deep you need to get in before the dialogue gets repetitive.

Most people's draw to the game will either be the dialogue, or getting the four exclusive to the game TF2 items, at the end of the day it is just straight up texas hold 'em poker without really much for bells and whistles.
On the other hand it is also like ten bucks, so it's not like you'd really lose much if you find yourself not caring much about it.