The rules for expressing past ability in English seem quite complicated. The traditional explanation distinguishes between general ability and ability on one occasion, and then gives verbs of perception and mental processes as exceptions (so we can say "I could smell coffee when I woke up this morning", or "once I got used to his accent I could understand him quite well"), but they often miss out other exceptions.

For example, why do we say "I didn't think I was hungry at first, but once I started I found I could eat a whole plateful"? "Eat" is not a verb of perception or mental process, but "could" sounds quite natural here.

To understand the difference between "could" and "was/were able to" for past ability we need to think a bit more about the semantic difference between them. It's true that "could" basically signals a general ability, while "was/were able to" signals ability on a specific occasion needs, but there's more to it than that.

Here is a more detailed explanation of the difference in meaning between the two:

"Could" focuses on the condition or state of being able to do something in the past. It doesn't focus on the action of actually doing it, and in some cases it may not even necessarily mean that it was actually done.

"Was/were able to", on the other hand, focuses on the reality, or the achievement of actually doing something on a particular occasion. It focuses on the specific ability to do something at a particular time, rather than on a general, ongoing ability.

In many contexts, the distinction isn't important. For example, we can say "I could smell coffee," focusing on the fact that that it was possible for me to smell it, or "I was able to smell coffee," meaning I actually did smell it, and in most contexts it wouldn't make much difference. If I walked past a coffee shop noticed a smell of coffee coming from the shop I could talk about it afterwards like this: "I could smell coffee coming from the shop," meaning that the smell was there for a period of time and it was possible for me to breathe in and smell it at any time during that period. Or I could talk about it like this: "I was able to smell coffee coming from the shop," focusing on the particular moment when I actually did smell the coffee. It doesn't make much difference.

But suppose I had been suffering from a cold and been unable to smell anything at all for the last week or so. Then suddenly, as I walked past the coffee, I noticed the smell of coffee. In this case I would be more likely to say "I was able to smell coffee," because I'd be focusing on the particular moment when I found I did actually have the ability to smell coffee, compared with the previous week, when i had lost that ability because of my cold.

Another explanation for why we sometimes prefer "was/were able to", rather than "could" is that "could" is often used to refer to the future. For example, when someone asks, "Could you ..." we are probably expecting a request to do something, such as "Could you tell me the way to Piccadilly Circus?" or "Could you turn off the radio?"

We can get round that problem by using "were/was able to" instead of "could" to express past ability on a specific occasion. "Were you able to sleep?" clearly refers to the past, whereas if we said "Could you sleep?" it is confusing, because "could" often refers to the future.

Even so, not all native speakers observe this distinction. Some native speakers will say things like "Could you sleep last night?" The English they teach in language schools is not always the same as the English you will hear in the street!

To sum up, then, the simplest way to decide whether to say "could" of "was/were able to" to refer to past ability is to ask whether you are focusing on the state or condition of something being possible (use "could"), or on the reality of something that actually happened (use "was/were able to"), or whether the distinction doesn't really matter (use either). As a secondary consideration, you might think about whether your statement using "could" might be confusing because people might interpret as relating to future possibility.

"Managed to" is fairly simple to use; we use it instead of "able to" in situations where someone actually did something and we want to emphasise how difficult it was to do. So, for example, we might say, "It took a long time, but in the end I managed to do it."