The smoke you saw was the water hitting the exhaust manifold and steaming up, no big deal there, you most likely got water down into the head area, coil area, fues box area, causing the lights and car to run like crap. Depending on the year it may have a cap (where the plug wires come out of to the spark plugs), it is not water tight, and any water gets in there will cause the car to run like crap.
Also with that force you hit the water at I would look at your radiator and make sure you didnt smash in all the cooling fins, if you did your not going to get any air flow through it and over heat your engine. Also you may want to take it in and atleast have your trans fluid flushed. It was undoubtedly submerged and any water getting in there will cause havoc, and rust the parts out, thicken the fluid turning it into goop, and can/will cause you alot of trouble down the road. If it was a automatic the trans wouldnt be that big a deal, but you have a manual, and under the gear shifter is nothing more then a rubber cover, if that is torn, you cant see for the interior trim is covering it, or is not secured properly, its not a boat so its not meant to be water tight, water will get into the trans at that point. And if you havent done this yet, pull the dip stick and check your oil and make sure you didnt get any water to go down into the crank, slim chance there, and if you did the oil will be overfilled and look like mayo, or thick and gray in color, but mainly overfilled for sure, which will cause the car to run like crap also, hell some cars wont even start if just a quart overfilled.
To dry the car out, if you have a garage, open the car up, all doors, trunk, hood, rent a de-humidifier from the local rent place, big commercial one for doing homes that have had a water leak, and put it in there with the car for a few days and let it pull all the water out, and cross your fingers it runs good again. If you cannot get to a one of them, on a nice sunny day put the car out there with the hood open, take off all the fuse box covers under the hood and make sure to point it in the direction of the sun all day so it keeps the sun beating inside the engine compartment and heat things up in there evaporating the water under the hood.
You can drive a car complete submerged under the water, if you have it completly waterproofed