In the Vampire Chronicles, Anne Rice explains (in The Queen of the Damned maybe?) that Akasha and the first vampires are incredibly strong because of their age. The longer they are "alive" the stronger they become until they are virtually indestructible. Marius says that at one point one of their guardians was so desperate to be rid of them that while they were sleeping he put Akasha and Enkil out into the burning sunlight to destroy them, but awoke in the morning only to find himself badly burned and Those Who Must Be Kept merely sunburnt. Apparently, whatever happens to them happens to all vampires (their descendants since they are the first).
ETA: Akasha and Enkil were originally humans and rulers of a kingdom called Kemet. When some unhappy subjects attempt to assassinate the king and queen, Akasha becomes inhabited by a demon called Amel as her soul is leaving her body. Her soul, now combined with Amel, reenters her body through her wounds and she awakens a vampire. She immediately turns Enkil into a vampire, and they become Those Who Must Be Kept.
Apparently, younger vampires can gain strength by drinking from older vampires. Lestat drinks from Akasha numerous times throughout Queen of the Damned and gains enough strength to be able to fly, survive sunlight, and a few other things I think.
ETA (again): I don't think Anne Rice mentions any specific weakness of vamps except sunlight, which, as we've stated, can be overcome if a vamp hangs around long enough and grows strong enough. This might be something she's changed as I've only read up through Memnoch the Devil.
I don't know about Blade.