Do oysters feel pain?
There are fundamental problems with defining what it means for an animal to feel pain, especially when the animal is a life form as different from us as an oyster.

I wasn't able to find any specific info online about oysters, but there is quite a bit of information that allows us to reason by analogy with related species.

Oysters are molluscs, and molluscs do have brains and sensory systems, but their level of sophistication varies a lot. Cephalopod molluscs, such as squid, octopuses, and cuttlefish, have extremely sophisticated nervous systems, and it has been argued (Peter Godfrey-Smith, Other minds, 2016), that we should think of intelligence as having arisen twice on earth through parallel evolution: once in vertebrates and once in the cephalopods. Cephalopods have sophisticated communication systems, and they can use tools and solve problems. There has been extensive research on pain in cephalopods.

So it's inherently pretty plausible that cephalopods can (in some difficult to define sense) suffer and feel pain, and by extension that their less advanced cousins the oysters can as well. However, the nervous system of an oyster is much more rudimentary than that of a cephalopod. A better analogy might be with snails, and there is some research on snails. They avoid damaging stimuli, have opioid systems, and respond to morphine and naloxone analogously to humans (e.g., showing less aversion to a hot plate when they've been dosed with morphine). So it seems likely to me that oysters can feel pain (for some reasonable definition of the word), but this whole area is one where people don't really know the answers to the questions or how to construct the philosophical foundations.