It is possible the oil could produce a not start, but unlikely. When I purchased my 91 EX years ago, oil leaked inside the spark plug wells, but the car started and ran fine. If you have spark at the plugs, then I would check to make sure you have fuel pressure at the fuel rail. If there is pressure at the fuel rail, make sure the injectors are firing when being told too by the computer.
Is the car cranking and just not starting?
Is the check engine light on? If so, pull the codes to see what the problem is.
Also, check all the ground connections including the one on the thermostat housing.
What about your mechanical and ignition timing?