Keep a clear head: if they are not doing anything it's not a problem.
Build a dormitory. No need to remove it later, since dwarves will automatically inhabit their own rooms and abandon the dormitory. It will serve as a buffer in case of large immigration waves. One bed per perso is too much, but 1 bed for 5 dwarves is okay.
By the third wave, your alcohol & food industry should be able to handle such disruptions. If they can't, you should expand a little your farms. If some of the newly built farms are useless (food overflow), you can just set it to be in fallow for the whole year until the need arises again.
To handle the excess brewing and cooking jobs, set one or two of the migrants to be designated cooks & brewers. 4 brewers/cooks for 80 should suffice.
Don't designate new rooms now. Wait until the dust has settled and your cistern is built.
This, plus:
Gather plants on the surface if you consider the surface safe; this can supplement or, under some circumstances, replace farms.
Trade for food and brewable plants with whoever sends you caravans. This can also supplement or even replace farms, often more easily than gathering plants will, provided you are producing something to trade with. Nearly everything in Dwarf Fortress can be worked upon to make it more valuable and therefore trade-worthy: bones can be turned into crafts just to trade for food, for instance. Whatever you seem to have an excess of, look on the wiki and see what you can make out of it.
Remember to make pots (they're smaller than barrels and hold more) so you have something to put food and drink in; you [EDIT:]can't[/EDIT] brew 100 urists of dwarven wine if you have only two more barrels to put it in. (What's more, you can make the pots out of rock if you've got unneeded stone lying around, and then if you wind up with a surplus of food and want to get stuff like caged (tame grizzly bears) from the elves you can actually trade them the food in the rock pots without them spazzing about deforestation.)
If anything isn't being produced fast enough, build a second workshop to make it on the double!
If you're low on
mandwarfpower, enable your migrants' labors to get the job done. Favor dwarves with higher skill in the labor in question, but don't forget that if there aren't enough skilled dwarves, you can enable the labor on some dwarves who have no notable skills so far and train them up. Keep in mind this is about having enough dwarfpower to produce what must be produced, not about prevnting there from being idle dwarves; contrary to popular belief, idle dwarves won't hurt anything. (Granted, it'd be nice if they'd spend more of their time cleaning, since they have nothing better to do... but nobody really knows why cleaning is so neglected even if there are dwarves not doing "more important" jobs.)
Another note: you don't actually need dining rooms with tables and chairs for your dwarves to eat, it just improves morale. There are lots of ways to improve morale if you find supplying the fortress with enough tables and chairs to avoid crowding complaints just too much.
And finally, don't worry if you don't have everything you need to take care of the migrant wave immediately, so long as you're working toward it. Most dwarves can survive a month or two of overcrowding or low food; it's perpetual overcrowding and starvation they can't handle.