What is the difference between keynote, invited, and oral conference presentations?

Having an invited talk and not having been invited is unusual, indeed. Maybe your professor was invited and passed the ball to you; the best thing to do is asking him/her.

"Oral" also is unusual for me (but maybe not in other fields). As noted in the other answer, typically the hierarchy is, from most to least prestigious:

• keynote/plenary: people who were invited to participate by the organizers, who may also be paying their expenses. Unlike the rest of the talks, they are not in parallel sessions or have a reduced level of parallelism. Sometimes, when there are no parallel sections, "keynote talks" are simply longer.
• invited: talks given by speakers that were explicitly invited by the organizers. Typically (but not always), the travel and registration expenses of these speakers are paid by the organizers.
• contributed: people who applied themselves for participation (and were accepted) and are going to give a talk, usually in parallel.
• poster: people who are going to present a poster instead of giving an oral talk. Sometimes people are given the option to present either a contributed talk or a poster.

I assume that "oral" means "contributed" here.

A keynote speech or presentation is a high-profile talk intended to be of interest to everyone at the conference, and is one of the selling points of the conference. Invited speakers are those who have been invited to give a talk by the organisers of the conference. My assumption is that 'oral' is just every other talk, i.e. speakers who applied to the conference and were selected to deliver their presentation.