Yeah, that will be difficult to explain! I will just add these comments to the three sentences that *might* help you out.
1) I heard the bomb go off.
2) I heard the bomb went off.
3) I hear the bomb went off.
I think you're right about 2/3. In both cases, it came from a source. And they both use the past tense in the second part. Whereas, 1 uses the present tense in the second part and is your direct personal experience.
Try adding the word "that". Which forces it to be something you got from a different source.
I heard that the bomb go off. <-- doesn't make sense
I heard that the bomb went off. <- makes sense
I hear that the bomb went off. <- makes sense
And the difference in tense in the first part in 2/3 changes the meaning slightly.
I hear... --> It is my understanding...
I heard... --> Someone told me directly or I read it, etc.
And finally, the following doesn't really work in conversation, right?
4) I hear the bomb go off. (this is like you're telling someone your own story) And then...
I hope that helps with some kind of explanation. :)