Oil air intake

Oil in most cases is normal, it circulates, in the recycled emissions, water could come from the rain, if intake pipe is low to the ground it can suck it in, if you have an aftermarket Turbo, it definitely comes from the air intake,

check and make sure push rod didnt damage head,rocker , valve or lifter [which i would replace]if all looks good clean repair and replace

You mean gas in the air intake??

Martin: and still no engine size stated, 4a or 7a toyota, it IS.
the oil there is normal. the PCV sucks , engine piston ring bypass
guesses and oil vapor. of the top of the engine, and burns the so the humans dont need to.
see your other anon post for lots of simple solutions.
that sputter is called MISFIRE.
misfire has many causes.
1: bad spark, needs a tune up. ever do the 60k mile this decade yet?
2: bad fueling, too much too little. (injectors leak? or clogged)
3: intake, leaks. vacuum leaks. you for got the DTC errors this post
4: bad compression on one or all cylinders.

do a full tune up first the wonder?

you most likely blew ur head gasket... needs to be fixed befor you keep drivng it or greater damage could be done

The oil in the intake is likely coming from the pcv valve- blowby. This oil shouldn't cause any stalling problem although it can give some blue colored smoke from the exhaust. A car that runs is worth fixing.

blown head gasket. the coolant gotten into the oil.

I would change the air filter, the valve and possibly the oil cap. Also, change your oil filter, it may be clogged. Keep an eye on it just to be sure there isn't anything more serious.

This is usually an indication of "blowback" caused by worn piston rings. How many miles on the engine? There is not a cheap solution if it is blowback.

Check if fuel or spark problem,..all engines need both to run...use starting fluid in air intake ,..if it runs very shortly-fuel pmp?,,ck for spark at spark plug,work your way back..also ck timing belt-intact? Kev-MN