I'm having eye surgery and there will be some bleeding. Do I need to stop taking fish oil supplements prior to that?

Yes. High doses of fish oil supplements can increase bleeding risks. Why take a chance on increased risk? Always check with your surgeon about these things.
No. If the surgery planned will go through an area that might bleed you should be off aspirin, blood thinners and nsaids. But fish oil will not affect this and can be continued.