Since others have addressed limiting migration, here's some tips for dealing with the large migration you already have gotten (or any you might get in the future).
1- Herbalism. Depending on your biome/current season, you can very possibly satisfy all of your short-term food needs by enabling the herbalism labor on several of your migrants and either setting up some plant gathering zones (assuming a not too old version of .40.xx) or designate large areas of the map for plant gathering. Depending on the available plants where you are, you might be able to supplement your booze stockpiles in this way as well.
2- secure a water source. Your dwarves might not be happy about drinking only water, but it will keep them alive until your booze production can catch up.
3- temporarily enable cooking on any seeds or plants which are edible cooked but not raw which you have plenty of, or for crops you don't intend to grow. You may have quite a bit of 'edible cooked' material sitting about that could be quickly converted into emergency food reserves. Just be careful not to deplete your seed reserves too far.
4- if 1 and 3 still don't get you enough food, you can put some migrants to work fishing/fish cleaning, or slaughter some animals that you could live without. Don't kill your last breeding pair of any animal you want to continue raising, but everything else is fair game in an emergency.
4- Put some of your useless migrants to work making beds/tables/chairs and digging out a dormitory and dining hall to accommodate your new surplus population.