Ok, 5w-30 and 10w-30 will not make a difference, run what you want. I choose 5w personally, because I like the extra protection during cold starts in the winter.
You are burning oil. You say it does it on acceleration, so it's probably rings. A compression test may not tell you anything. If I had to take a guess, you probably have stuck oil rings. You'll still have good compression, but you will burn oil pretty good. I've heard that you can get them unstuck by running some sort of crankcase cleaner through it, ie seafoam. I personally don't like crankcase cleaners, because they aren't nice to your seals, and they knock off a lot of dirt all at once. Your also suppose to change your oil like 1000mi or so with synthetic for a while until it starts looking cleaner.
You might try just the second part, idk if that will work though.
On my accord i just replaced the rings and cleaned out the ring seats, and the thing ran like a dream. So much smoother now, and better power.
