Here we go. Let’s see if I can translate the grammar dictionary’s clarifications into plainer English…
S1たらS2 = “when S1 is satisfied, S2 takes place” – it’s why it’s sometimes translated as “when” rather than “if”. I’m not sure what you mean by it’s used for past occurrences, but while S1 is always in the past relative to S2, both events may be in the future for the speaker. Or both may be in the past. Or just S1.
S1ならS2 = “supposing S1 were to be true, then S2″ – it’s something of a hypothetical if. You can’t use it for something that’s guaranteed to happen, like “if it’s 10 o’clock” (because there’s no need to suppose), if it’s based on random chance, like “if it rains tomorrow” (because it’s not possible to suppose), or if it’s something that you already know for certain to be true. If S2 is past, S1 must also, and the sentence becomes something like “if S1 had happened, then S2 should have”
S1ばS2 = “if S1, then S2″ – the plain old conditional form. S1 represents a condition under which S2 will hold true.
S1とS2 = as already mentioned, “if S1 happens, S2 is a natural and unavoidable result”.