While helen's answer addresses the meanings of some of the particular phrases and idioms, the key to why this is funny is the long-running TV game show Jeopardy!
The SNL skit mimics the format of the game show, and uses the name of the host (Alex Trebek). If I recall correctly, the disruptive player in the skit is pretending to be actor Sean Connery.
The skit is, as far as I can tell, funny because the disruptive player disrespects the play of the game, misinterprets the clues to be crude phrases, and continuously insults the host. This kind of social humor is difficult to explain, especially because I don't get most of it.
The humor is situational and not really a matter of language.
I suggest you do not behave in this way or use these phrases. The phrases are not funny in isolation, and at least "nancy boy" is likely to be offensive.