I'm not sure why my furnace keeps coming on. I have oil heat and I had an older thermostat so I figured that was why so I went and replaced it with a brand new one and am still having the same problem.

(I have no zones, so only a 2 wire hook up, I didn't mess it up)

I have it set at 55 to be sure there's no reason for it to come on, it is reading the temperature is 70 degrees and my furnace continues to periodically kick on throughout the day and I can feel that the vents are putting out heat so this is not just turning on for the hot water (oil as well) and still shouldn't be any reason for that because I haven't used any hot water and for the purpose of this test I went and turned down the hot water as well.

So, what do I try next?

From what you are saying it sounds like you have hot water heat. If so, you could have a zone valve sticking open or a sticking flow control valve. If it's only getting to 70*, I doubt the circulator is running. If it were, it would probably get much hotter than 70*.