If you close as "off-topic, other", you'll be asked to enter some text. That text will become a comment on the question, and others who vote to close will see your custom reason as an option that they can also select. I recommend a comment of the form "off-topic because it is about X, but I suggest migrating to (site name)". None of this automatically notifies moderators, but we're a small site so we'll probably notice anyway. Feel free to flag if you think the situation is urgent or if you fear that it hasn't been noticed via the closure.
(A general note about closing: we are very reluctant to unilaterally close questions unless it's really, really clear-cut. If you have close-vote privileges please cast a vote in addition to any flags you raise! It really helps to make it clear that this community is run by the community and not just by a few people with diamonds after our names.)
You asked how migration works. First, Stack Exchange doesn't generally define any custom migration targets for beta sites, so usually the only built-in option is meta. Somebody must have made an exception to get EL&U onto our list. So it's best not to assume that we'd be able to get other destinations on that list.
Migration is done by moderators after it's determined that a question doesn't belong on our site. Note that just because a question could also be asked somewhere else doesn't mean that we'll migrate it; we're very possessive of our on-topic questions. The asker decided to ask here, so if the question works here we go with that. Migration is for questions that don't fit here but do fit somewhere else.
Finally, if we're going to migrate a question we try to make sure it's in decent shape first -- it's impolite to just throw a question over the wall if the receiving site is then going to have to do a lot of editing or ask the author for clarification. So even if we're closing a question, if it's being suggested for migration, please try to help edit it if you can. Don't worry about tags (those are different on every site), but please help with grammar, formatting, clarity, incorporating new information from comments, etc. Thanks!