Help with automotive/engine/exhaust?

I own a honda accord 04 today I tried to turn it on it wouldn't start for a moment I had to give a few tryis to turn it on a hour later it began to let out white smoke from the exhaust a lot and the engine was smoking to what do you guys/gals think its the engine or a leak. And another thing is I was putting in oil to I spilled some to the engine and some steering fluid got mix in to could that be the problem or something major?

White exhaust smoke is generally caused by coolant burning in the combustion chamber. The cause of which is usually a blown head gasket, cracked cylinder head or a crack in the engine block itself. Hopefully yours is the lesser gasket issue.