I'm unable to start any of the side quests for the vampires in Castle Volkihar. Every time I talk to a NPC in the castle they keep saying the same basic dialogue instead of offering me quests. Even as i played through the vampire side I couldn't receive any side quests and when I finished, it still didn't work. It's weird because I played through the Dawnguard side on my first playthru and their side quests worked fine.

You have to finish "The blood stone chalice" first.

I did and it still won't give me the side quests.

Does anyone have the option in their dialogue menu "What can I do to help" for you to click?

Nope just the same dialogue no matter what I do.

If you are on PC you could first try setstage DLC1VampireBaseIntro 200

I'm on the xbox 360

I haven't had enough experience with Dawnguard to know what kind of a bug this is, so I would suggest reverting to an old save.
Some other thoughts: I suppose you are still a vampire and haven't been cured? Have you spoken to everyone in the castle, just in case there is only one with the "What can I do to help?" option? Serana as a follwer is known to be buggy, do you have her as a follower, or know where she is? (If she's stuck somewhere or you are bugged with a follower other than Serana waiting for you outside the other entrance to Volkihar Castle, it may have bugged you somehow )

IDK. I dont have serana as a follower or anyone else. I've tried everything from waiting an in-game month to attacking everyone in hopes that they just needed a little push. But alas they wont offer any quests. The only thing I haven't tried is uninstalling Dawnguard but I fear that may corrupt my saves as I've finished most of Dawnguard quests.

Your best bet is still to revert to an old save, but you might also try an experiment of making sure you can get the buff from the Bloodstone Chalice. Also if you are still on the Vampire side MQ, you could continue doing those quests, which may update something. If you have finished the main questline, I would also suggest heading back to the Soul Cairn and speaking to Valerica (I won't say any more just in case you haven't finished all of the quests).

I hope you have an old save you can go back to...