Both are based off mangas right? Do I have to read the mangas for either series or can I just watch the OVA and animes and not have to read the mangas?
You can watch any anime and its OVA(s) without reading the manga. However, usually manga do contain extra content that aren't covered in the anime and OVA(s). So while you don't need to read the manga to watch the anime, you can for an extra bit of info/story.
So you could read the manga on top of watching the anime and OVA(s) for Read or Die, but it's not necessary to go through both. It could be fun though.
According to Wikipedia:
[The OVA is] based on the Read or Die manga series... [It] is a continuation of the Read or Die storyline, taking place a few years after the events of the manga.
R.O.D the TV is a 26-episode anime TV sequel to the Read or Die OVA
Incidentally, R.O.D. started as light novels and manga published at the same time.
As with all OVAs I've seen, while you may be able to watch them and get some understanding of what's going on without reading the original source material, they are usually short and made on the assumption that people who already like the source will be the audience. Therefore, they tend to rush through exposition, and even skip over details that they assume the audience is already aware of. As I remember (it has been a while since I watched) it seems that in the case of the R.O.D. OVA, this meant they had very little explanation of the events that happened a few years before. So probably you would get more out of it if you went back and read the manga or light novels.
It should be borne in mind that the Read or Dream manga is not in the same canon as R.O.D the TV. The sisters meet and adopt each other in a different way. Hisa has a different history and meets the sisters under different circumstances.
On the other hand, I'm not aware of any contradictions between the Read or Die manga and either of the anime series.