I have a 91 Accord that is burning oil somehow but not a visible leak. The dipstick is dry after adding 3 quarts 3 days ago. What should I look for?

Sorry about the misunderstanding and please do not take this wrong, but that is a lot of oil and your symptoms do not cover that kind of consumption. I am wracking my brains trying to work out how so much oil could be burnt up in just 30 miles, that is almost the same amount as the fuel you would use in that distance. It cannot get into the gearbox, if it got into the cylinders it would smother the engine, if it was leaking out you would have pools of oil everywhere.
Suggestions? Check you spark plugs to see if or which ones are very oily. Have a look if there is oil in your coolant? Check if there is any signs of oil in your exhaust pipe. If the smoke is predominantly when you accelerate, it would be due to worn rings - normally, but that would only be in the region of a quart per 500 miles or so.
Come back to me with your findings, I will give this some more thought and research in the mean time. Sorry about the misunderstanding and please do not take this wrong, but that is a lot of oil and your symptoms do not cover that kind of consumption. I am wracking my brains trying to work out how so much oil could be burnt up in just 30 miles, that is almost the same amount as the fuel you would use in that distance. It cannot get into the gearbox, if it got into the cylinders it would smother the engine, if it was leaking out you would have pools of oil everywhere. Suggestions? Check you spark plugs to see if or which ones are very oily. Have a look if there is oil in your coolant? Check if there is any signs of oil in your exhaust pipe. If the smoke is predominantly when you accelerate, it would be due to worn rings - normally, but that would only be in the region of a quart per 500 miles or so. Come back to me with your findings, I will give this some more thought and research in the mean time.

Looking at literature, normal oil consumption on an average car with average wear should be about 1 pint in 2700 miles. Sorry if this sounds like an interogation. Before you put the oil in was it showing on dipstick and did the oil light come on at any time like going around corners or braking etc. Another thing it could be is the cylinder head leaking between one of the cylinders and an oil passage, but that would mean the engine would be running on three cylinders and still smoking. Everything I saw says that high oil consumption is caused by leaks, worn valve guides and seals or worn piston rings. With the engine running, can you remove the oil cap without getting a shower of oil or have oils shooting out of the dipstick tube when you pull the stick? Looking at literature, normal oil consumption on an average car with average wear should be about 1 pint in 2700 miles. Sorry if this sounds like an interogation. Before you put the oil in was it showing on dipstick and did the oil light come on at any time like going around corners or braking etc. Another thing it could be is the cylinder head leaking between one of the cylinders and an oil passage, but that would mean the engine would be running on three cylinders and still smoking. Everything I saw says that high oil consumption is caused by leaks, worn valve guides and seals or worn piston rings. With the engine running, can you remove the oil cap without getting a shower of oil or have oils shooting out of the dipstick tube when you pull the stick?