1. All social dynamic games are great and usually handle high player counts, The Resistance and Coup are especially good but a little longish to play. I would recommend One Night Ultimate Werewolf as a great one that plays quickly so players can rotate in and out.
2. Cardgames that people can pop in and out of without drastically affecting the game state are ideal. Spot it, Set, Ghost Blitz, Fluxx, and Anomia fall in this category. Jungle Speed kind of does and works well, I HIGHLY recommend a super simple card game called Loonacy that plays fast frantic and everyone wants to get in on the next round of.
3. High player count "thinky" games with fairly straightforward rules are also ideal as people can wander in and sort of adopt a team and start playing. The game concept is probably the king of this and is more of an activity than a game but can keep a group going for hours. A recent release called Codenames is also excellent for this but a little hard to find right now.
4. Push-your-luck games work well for these situations and people tend not to feel as bad if they lose just because of luck or because they got greed. Suggestions include Can't Stop, Incan Gold, or X-Scape.
5. Simple bidding style games also work well and remind people of poker which they like. The best two for this category and age range would probably be No Thanks! and For Sale.
6. Dexterity games are GREAT for this. Check out Pitchcar, Crokinole (especially for you Canadians), Dancing Eggs, Tok Tok Woodman, and really any dexterity game without a muktzah element.
Time's Up! (particularly the Title Recall version) is simply the best party game ever invented.
There are many other great party games that won't work on Shabbos for various melachah reasons.
My top 3 on this list for NCSY settings are Spot it, Set, and Concept because they can all handle any number of players, can be taught in minutes or even seconds and players can walk in and out of the game at will without ruining it for everyone else.