With respect to those in particular, I can't think of any experience off-hand which would raise my confidence in any of them high enough to be worth considering, though that's not to say that such experiences don't exist or aren't possible... I just don't know what they are.
Huh. That's interesting. For at least the first two I can think of a few that would convince me, and for the third I suspect that a lack of being easily able to be convinced is connected more to my lack of knowledge about the religion in question. In the most obvious way for YHVH, if everyone everywhere started hearing a loud shofar blowing and then the dead rose, and then an extremely educated fellow claiming to be Elijah showed up and started answering every halachic question in ways that resolve all the apparent problems, I think I'd be paying close attention to the hypothesis.
Similar remarks apply for Jesus. They do seem to depend strongly on making much more blatant interventions in the world then the deities generally seem to (outside their holy texts).
Technically the shofar blowing thing should not be enough sensory evidence to convince you of the prior improbability of this being the God - probability of alien teenagers, etcetera - but since you weren't expecting that to happen and other people were, good rationalist procedure would be to listen very carefully what they had to say about how your priors might've been mistaken. It could still be alien teenagers but you really ought to give somebody a chance to explain to you about how it's not. On the other hand, we can't execute this sort of super-update until we actually see the evidence, so meanwhile the prior probability remains astronomically low.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.