Toyota Repair: 2001 toyota avalon, 2 quarts, valve seals

Question
I was visiting family I drove home and my oil light came on the next morning I had my husband check the oil and it was very low we put 3 quarts of oil in it but we did not realize it was synthetic oil so about a week later I took it in for an oil change and they told me that it was about 2 quarts low and that it was not showing on the dipstick so they changed the oil, oil filter, and all, but a few day later it started smoking when you start the car.  In the morning when you start it for the first time it pours smoke from the exhaust pipe until it warms up after it is driven for a while and it heats up it stops smoking  so I do not know what they did to it to make it smoke, and it seems to be getting worse my dad looked at the car when I told him about the oil because i asked him to cause there is no oil spots on the ground so i just asked him what it could be and we found that the head gasket was messed up when you take the oil cap off the head gasket it looks like slug and so I am just trying to find out what is wrong with my car

Answer
Since there is no oil leaking externally the engine is using it which is what causes the blue smoke, in most cases the valve seals are the cause of the smoke but if there are a lot of miles on it, more than 100,000 and has not been mainyained very well and there is sludge in the oil cap then the piston rings may be worn as well, either way it's an expensive repair.