I, mamadeb, do solemnly affirm that my favorite HP character is Remus Lupin and my least favorite character is Delores Umbridge. The mere thought of them doing naughty things together makes me whimper. However... given sufficient crack and an infinite number of monkeys,* here's how a Lupin/Umbridge shag might happen (though I sincerely hope it never does, and if it does, I just don't want to know).
Necessary plot device or deus ex machina: "Shag or die."
Who makes the first move: Lupin because while he hates her and would probably rather die himself, he can't let her die. Much as he would want to.
Positions and/or kinks: Umbridge is a closet sub, so the fact that Lupin would have to tie her up to have his reluctant way with her would turn her on - and turn her into what she would percieve as a little sex kitten (and he'd percieve as his worst nightmare.)
Afterglow: She will fall in love with his masterful behavior and aloof nature and try to win his regard by changing all discriminatory laws about werewolves and then intelligent magical non-humans. In return he will hold his nose and have kinky sex with her until finally disgust at himself and his neverending nightmare of a life causes him to eat a silver bullet. She will then style herself Madam Lupin and wear pink trimmed black forever.
Would I actually read or write this? Umm...