Is "Read or Die" based on manga? 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.