Is there any difference between these three phrases?

Essentially, yes, though I guess each of them have very slight differences to me. I just woke up, so apologies if any of this is incorrect.

I hoped to have finished my homework yesterday

I'm on the fence as to whether or not this sentence makes sense as written. It sounds okay at first glance (or it did to my 7 AM brain, at least), but I personally think it would sound better to say "...to have finished my homework by yesterday". If you say that, it emphasizes that you had been hoping for a long period of time that your homework would be done by whatever day yesterday was.

I hoped to finish my homework yesterday

A basic past-tense sentence without any perfect aspect. This sentence doesn't specify any sort of time frame aside from the past, so we can't make further judgement about the meaning. It's correct, but vaguer than the others.

I was hoping to finish my homework yesterday

Saying this, to me, mostly emphasizes that the "hoping" went on for a while, but then the situation might have changed for some reason that made you not hope for that anymore. Like, say you were making good progress on your homework yesterday, and you had been hoping for the whole day that you'd get it all done. But then your dad called you and told you to mow the grass, which took up the rest of your day, and you didn't get to finish it. I might use it in cases where the hoping never changed, but in that case, I think it means the same thing as your second sentence.

You would probably get better answers in the future if you asked /r/englishlearning and /r/grammar, by the way. This place isn't the best place for asking questions about specific languages.

/r/languagelearning Thread