We currently had a new turbo put into a 2000 Volvo S40, 110k miles. Initially, the car would smoke when accelerating hard with the new turbo. After a few weeks the smoke never occured again and the car functioned normally. Than, the car stalled at a stop sign and as it was being pushed to a safe location, the engine caught fire. The fire was put out with an extinguisher and the insulation that lined the hood (?) was burnt through. I am wondering if any of this could be because of improperly installed turbo by a mechanic or something due to the age of the vehicle. The volvo still runs, though it sounds aweful. It revs irradically.
As @Moab said in his comment, an oil leak from the turbo supply or return line could be the cause of the fire. Oil is nicely combustible, and since your turbo a) gets very, very hot, and b) is right on top of the exhaust manifold, a leak is in the perfect place to catch fire.
If the turbo issue has not been corrected, you may have another fire soon. Fix it before driving the car. You do not want to be trapped in a car going 70MPH when it bursts into flames.
The fire could have harmed any number of things under the hood that can cause the erratic engine behavior. Look at your wiring harness, specifically the lines going to the O2 sensors, ignition coils and other sensors (IAT, MAP and/or MAF, etc.) Look at any plastic parts that may have melted. Check your battery cables (and others) to see if the insulation was damaged, as that can lead to a short. If the insulation is damaged near a grounded part of the engine or frame, and the bare wire exposed due to missing insulation touches it, odd things will happen.
Check all your vacuum lines. A vacuum leak will make the engine unhappy.
Depending on how hot it got under the hood, you could have warped or cracked the head and/or block. However, if that happened, I'd expect the car to be a smoldering pile of slag, not just running rough.
Another option: get the shop that installed the turbo to pay to replace the whole engine and harness. (Admittedly, given your experience so far, I'm not sure I'd let them do the work.) If they're at all reputable, they should cover this.