C, E, G, I.
A doesn't work because "can" refers in such a context to his capacity to know, not the likelihood that he already does. It's grammatically correct, but it's such an obvious statement that it's meaningless.
None of the negative versions work because in that case, "something" needs to be replaced with "anything". It's very rare to "not X something", but in those occasional cases "something" is referring to a single thing that is not "X", and it would normally be formed in a way that puts "X" closer to the end.
If you were to replace "something" with "anything", though, B, D, F, H, and J would all be fine.
Of course, all of these have completely different meanings:
"He was here last night. He can't know anything about the accident."
Suggests that he was or is in a circumstance that prevents him from possibly knowing anything.
"He was here last night. He may know something about the accident."
Indicates that it's possible that he might know something, but might not necessarily be likely. "May" can also be substituted with "might".
"He was here last night. He may not know anything about the accident."
Indicates that it is likely he does know something, but plausible that he doesn't know anything. "May" is more likely to be substituted with "might".
"He was here last night. He must know something about the accident."
"He was here last night. He has to know something about the accident."
Both of these are identical in meaning; they indicate a very strong belief that he knows something. The latter is a bit more emotional, I think.
"He was here last night. He must not know anything about the accident."
An explanation that some known fact suggests that he doesn't know anything. I could see this in the context of the person being talked about carrying on with his work like normal last night rather than investigating the accident as it occurred, for example.
"He was here last night. He shouldn't know anything about the accident."
An unlikely expression, but if it were spoken, I imagine it would probably be the people responsible for the accident noticing and being surprised by the fact that he is here, then reassuring themselves that he didn't see anything.
"He was here last night. He doesn't have to know anything about the accident."
A statement that it would be perfectly reasonable for him to know nothing about it.
