how do you enter the streeties club house?

You need to max out all points of the rep group whose club house you want to enter. For example, if you want to enter the club house for the Streeties, you need 10 rep points for the streeties. When you have all 10 points, speak to the group leader and they'll give you the key to the club house.

To get 10 points, you need to complete all missions for the rep group, befriend all members of the group (at least 50), be very close to the leader (100), find the group's trophy to deliver to the leader, and it also helps to live in an area they like (for instance, a house in Urbania for streeties, the skyline penthouse or the glasstown townhouse for richies, etc), and to be on the bad side of members of the opposing group (-5. Streeties are rivals to Richies and Nerdies are rivalled to Artsies and vice versa). Ideally you should do this for the rep group you are currently in, but if you want to switch rep groups, talk to the leader after you've max out the rep points of their group.

For example, if I'm a richie initially, and I want to become an artsie, I have to speak to Roxanna after maxing out my artsie rep points. She'll then ask me if I wanna join her, and when I say yes I will then be an artsie from now on. If I wanted to change back to a richie, however, I can do the same (with maxed out richie rep points) by speaking to Luthor.

The minigame in the club house can be unlocked by becoming a nerdie. Eventually as you gather nerdie rep points, you can unlock the xizzle ability "Spell Champ" to buy in order to play the minigame with.

The Nerdies trophy is located in the parking lot of the carnival. There is a tree next to the booth near the edge of the parking lot, it is in the tree.

The Artsies trophy is located in the bayou. Go to the part of the bayou where the two man-eating plans are by each other. There are some bushes/plants/tress behind them, this is where the trophy is located.

The Streeties trophy is in the cemetery, I believe in the part right after you exit the mausoleum. It's by one of the tombstones.

The Richies trophy is on the second floor of the Glasstown mall, I don't remember where though, sorry.