The basic idea of the past continuous is to describe an action that is ongoing and incomplete, usually an ongoing action that is interrupted by another action (which would be in simple past):
While something was happening, something else happened.
For example, this would be entirely correct:
The dentist was still working with another patient, so I sat in the waiting room.
This is a little unclear, because you presumably kept sitting after the point in time described, so the sitting could be thought of as incomplete. But the continuous activity provides an ongoing context for the simple activity; it encompasses or encloses the simple activity. For example, we could also say this:
I was still driving to the dentist's office at the time of my appointment, so the dentist worked with another patient.
Now, we could simplify this a bit by changing the simple behaviors so that they don't imply ongoing activity:
The dentist was working on another patient, so I left.
I was sitting and reading in the waiting room when the dentist came in and told me she was ready to see me.
There are a few usages that might seem a bit different, but are really the same:
I was planning to go out to a party but I decided to stay home and watch a movie instead.
I was wondering if you might be able to lend me a dollar.
In the first case, the planning is ongoing, and interrupted by the decision to stay home. In the second case, the wondering is still ongoing at the point of asking, so it is more grammatically correct to use the present perfect continuous ("I have been wondering if you might be able to lend me a dollar"), but idiomatically we use the past continuous in this situation.
Best Answer
He said is the simplest way of describing the words that someone spoke. This is the most common. The actual words spoken would be "I'm going to leave soon". You could use this to describe what someone said at any time, even after they have left.
He says is talking about what the person means, or the ideas that they have right now. It would be used to imply "If you were to ask him right now, this is what he would say". In practice, there are many situations in which both "He said" and He says" are both possible. But if the person has already left, then you couldn't use "He says".
He was saying adds the continuous sense to he said, it suggests that he spoke at length, and so "he is going to leave soon" is just a summary, not directly quoted speech.