In Bran's third chapter in A Dance with Dragons, we see that he can easily warg into Hodor, without anyone realizing. As soon as he smiled a lot and said some Hodor's now and then.
Can Bran make Hodor say anything he wants while he is in his body?
In the novels so far, Hodor hasn't said anything more than "Hodor".
However, I suppose that the problem is with his mind, not with his phonetic system, so, if Bran gets enough control of him, I bet he would be able to speak through the gentle giant.
Bran cannot make his direwolf speak, of course, as a wolf lacks the articular capacity on their throat, mouth, and tongue to pronounce articulated sounds like words. Bran, however, is able to howl when possessing the direwolf.
Hodor's mouth, tongue, and throat are fine; he's able to pronounce words (although he just pronounces one); it's his mind that is the problem. He is unable to use that mechanism to pronounce any other word. If Bran takes control, his mind would know the words and the knowledge of how to pronounce them, coupled with a body with the correct muscles to do so.
If he hasn't done it yet, it's probably due to the fact that he has only taken control of Hodor in tense action moments, and because is a lot harder to control a delicate and complex system like the mouth and tongue than just walk and move the arms.
In summary, it hasn't happen yet on the books, however I bet he can.
Check out this article: http://io9.com/neuroscience-explains-why-game-of-thrones-hodor-can-onl-1593383062
According to it, the reason that he can't say anything other than "Hodor" may be because a part of the brain called " Broca's area" which is linked to speech production is damaged (has lesions). If that's true, even though Bran takes control of him, he can't remotely fix-heal his brain.
Unless magic then I guess he can.