Is there a maximum size for a black hole?
As far as I understand it black holes radiate Hawking radiation
That's what people say, but we have no actual evidence for Hawking radiation. However even if Hawking was 100% correct, as Rob said, Hawking radiation has less and less effect as the black hole gets bigger and bigger.
and probably gravity waves
A black hole on its own won't emit any.
which over time causes them to lose mass and eventually evaporate after almost unfathomable amounts of time.
There's no scientific evidence that a black hole will disappear. However there is scientific evidence that black holes exist. There's definitely something very small and very massive at the center of our galaxy:
I've also read that black holes eventually have difficulty gaining size after a certain point because gravitational forces working in a black holes accreditation disk can eventually begin ejecting in-falling matter before it can be absorbed.
Yes, black holes are said to "choke" if they try to eat to much at once. See the physicsworld article Supermassive black hole struggles to swallow Milky Way. There are other issues to do with gamma ray bursters meaning black holes are messy eaters, but they still "eat", as it were.
While I know black holes can become quite massive, that leads me to wonder if Black holes have a maximum possible size where they will begin to immediately radiate any additional mass that's added to it. Or can a black hole effectively expand forever as long as the supply of matter is greater than the effects of radiation and ejection?
It's the latter. Imagine you're near a supermassive black hole. It's so massive that any Hawking radiation is negligible. It has no accretion disk because it's eaten everything or blown it away. What happens next? You fall in. So that black hole gets bigger.
Is there effectively a size limit to black holes?
No. If there was, and the black hole in the above scenario had reached it, you wouldn't fall in.