Poor running when cold conditions

What conditions would make a 2.5 L 4cyl run poorly when cold and not when warm. Stalls and misses till it's warm, then runs like a top. Only getting 15 MPG and the computer says O2 sensor stuck on lean. It's a new sensor. Checked vacuum hoses and fixed a leak, changed the PCV valve and put a new rubber elbow on it that was cracked. Cleaned carberator and it looks quite good. Put a new fuel filter on - it was quite plugged. Still acts the same. Funny thing about the timing was when we hooked on to number 1 wire and then number 4 wire, there was a big difference in the timing values. Mechanic said it should be about the same. Is a thing called the cranskhaft position sensor at fault to do this? Since it only does this when cold, can you put the blame on things like the MAF sensor or the idle control sensor? If the fuel pump were bad, wouldn't it run poorly when warm and cold both? Brand new motor and I'm getting tired of it not running right. If the O2 sensor was poisoned by gasket goo, would it do any good to change it, or would you have to get rid of the gasket goo first? Sure appreciate an answer.

So, if you want to know, the stalling was fixed by gapping the plugs properly. The mechanic also noticed that the head gasket was leaking. This was on a new motor. This is probably what fouled the O2 sensor too.