Should we downvote questions that have been closed (to keep the front page clean)?
I would follow the guideline on the tooltip of the voting controls:
This question is unclear or not useful
If you strongly believe that to be true (strong enough that you're willing to absorb the minimal -1 rep cost of casting a downvote) then you should cast your vote that way.
A question might be well posed even if it is off-topic. Since apparently many "wrong-posters" feel offended by heavy downvotes, I think we should not necessarily do so. We should acknowledge that the question was posed in a good way and encourage reposting on/moving to other sites.
In case of moving, will votes be moved, too?
Questions that are both off-topic and badly posed should feel our full pressure, though.