The better upfront information given in the original post request usually leads to better and quicker solutions.
Let's try again for background info.
What year 318 are you working on?
What kind of hours has this engine have on it?
What was the oil pressure when running?
Why did you decide to pull the rockers and pushrods? In other words, what were the symptoms of the engine prior to tearing into the engine?
Are these "3-4 tappets" all in the rear of the engine, at the front, all on one bank, or random in the block?
Is the oil coming out of the lifters themselves or from between the lifter and block lifter bores?
Oil pressure will find the point(s) of least resistance. Cranking alone may not provide enough volume especially if the pump and other components are worn.