How do I get better at giving talks/presenting research? I read many papers and try to present some of them at a reading group of some sort in my department (these are all quite informal). Both my most recent talks were what I consider quite bad, and I really want suggestions to get better. 

I only choose to present papers that I understand reasonably well, but when I start talking about them, I often fumble, fluster, and feel the need to constantly look at my notes, even though I know the math (I am in Theoretical Computer Science). I often start saying a sentence, then pause and start afresh since I forget to add a "modifier" like, "given an epsilon > 0" or something like that. 

I really don't know how to get better. Due to classes and research, I didn't get time to rehearse my talks before. I also recently gave a formal talk as part of my Qualifying Exam, which went very well (as the committee told me, but also, I felt it too!), but I'd rehearsed it six or seven times before the final talk. 

I can't spend so much time for every talk. So I want to know if there are any suggestions to get better at talking. I know stage fright isn't an issue as I'm quite an outgoing person. 

EDIT: These are all whiteboard talks.
One important thing, for both casual talks and more formal talks, is your notes. Too many details and you can't use them without interrupting the flow of the talk, too little and you can get lost.

After some time, I converged to the following solution. I usually prepare one or two pages of main notes, not too densely written, with the main items I want to speak about and large signs for important things to mention at some point. Beyond two pages, I just end up caught in the moment and diverge from the planned path and improvise too much.

Usually there are some points where I could need a complicated formula, a precise statement, or a question might occur that needs one of these in order to be answered; then I simply make a mark (circled capital letters of color) where they might be needed, and write down the details along with the same mark on a second set of more detailed notes. Then I can refer to these when needed.

Another, general advice: be careful of what you do not like in other's talks, think about why, and be sure not to do that. The flaws of talks are often broadly shared, and this can only happen because we do not realize we do exactly what we blame others for.