Honda accord 2008. Motor oil?

I've been using honda oil 5w-20 but my car is burning oil now, my muffler tip is black, which oil should I use now? Would amsoil or royal purple 10w-30 be a good idea?

If your owners manual says 5w-20 use 5w-20

Always go thicker than the manual says, because they want to advertise the best mileage, and don't want the camshafts or bearings to last as long as they could. I would never recommend anything thinner than 10W-30, and as there's wear over time, you must go even heavier. I prefer Castrol myself, but I have heard Royal Purple is good.

Mobil 1 Extended Performance however performs MUCH better than the other variants they offer. If you need something not too expensive that is available at Walmarts in 5qt jugs you can grab that.
OR
You will try to use 5w-30 synthetic oil, it helps prolong the engines life, Which will cover both summer & winter.
Amsoil 10w30 that is too thin of an oil will cause havoc on heavy springs and high lift cams.