Before I answer, I'm going to correct your 3rd example to:
- I would have left yesterday.
"I would leave yesterday." does not make sense because "would leave" is present and "yesterday" implies that the action is in the past.
After making that correction, all four of the examples you provided do mean approximately the same thing. They are all used to state the circumstances that surround a statement made about the past. Stated alone, none of the four form a complete thought. They all require an additional clause that explains what happened afterward. That being said, 1, 3, and 4 are approximately the same (the only differences being in nuance) and 2 is different.
1. I was going to leave yesterday
This expression implies that you decided to leave at some point in the past, you were just about to actually leave, and something stopped you. It is almost always followed by "but". In addition, this expression has a slight "blame shifting" nuance to it.
I was going to leave yesterday, but I couldn't find my car keys.
I was going to leave yesterday, but I had too much work to do.
3. I would have left yesterday
This expression also implies that you decided to leave at some point in the past (unclear about when) and that the leaving did not happen. This is very similar to "was going to leave" but slightly different.
"was going to leave" sounds like you are about to start a story, "would have left" sounds like you are about to state a reason.
"would have left yesterday" conclusively states that you did not leave "yesterday". "Was going to leave" suggests that you did not leave "yesterday" but is only explicit about the specific instance in the main clause. It leaves the possibility that you left later in the day open.
"would have left" is not clear about the time that you decided to not leave. "Was going to leave" suggests that you decided to not leave at the last minute (right before you actually left).
"Would have left" is almost always followed by "but".
I would have left yesterday, but my car was stolen.
4. I was about to leave yesterday
This is interchangeable with #1. The only difference (and it is a small one) is that #4 sounds like you were a little closer to actually leaving than #1.
I was due to leave yesterday is much closer to #3 than #4. They both are not explicit about when you decided not to leave, they both are usually followed by "but", and they both conclusively state that you did not leave yesterday. As far as differences, "I was due to leave" is rather formal sounding. It has a feeling that you are abiding by a schedule set by someone else. It doesn't come up in non-business conversation often.
2. I was leaving yesterday.
The first three examples have a strong contradicting tone. They all imply that you did not actually leave. This one implies that you did in fact leave (but bear in mind, it doesn't imply that you got very far). It is usually followed by "when".
So to summarize, we can approximately order the 5 expressions by the time you decided to not leave (earliest first). I'll use the image of a man about to leave his house to illustrate (bear in mind that in actual usage, the time frames can blur).
"would have left", "was due to leave" - (not explicit about when)
"was going to leave" - the man walked up to his door and changed his mind.
"was about to leave" - the man opened his door, started to take his first step out, then changed his mind.
"was leaving" - the man succeeded in taking his first step out and is somewhere between his door and out of his driveway.