What are the oldest Tantras

The oldest ones (as per written records) belong to 7th-9th century. Oldest Hindu and Buddhist were concurrent. These were kashmir shaiva tantras and contained the essence of shaktism in them.You can read Alexis Sanderson on the matter. Yamalas are one of the oldest sets of pure tantrism most of which are now lost. Kaula Jnana Nirnaya (Matsendrayanatha) is said to be one of the oldest extant texts of the kaula school. Older and complete buddhist texts are better preserved like SriHerukabidhana (a.k.a the famous Cakrasamvara Tantra). The reason is Hindu tantrism was studied in select pockets of the country, one being Kashmir which took heavy onslought of Moslem Barbarians, while Buddhist Tantrism was studied in many monesteries and transmitted to Tibet well in advance.

Authoratative is tricky word as these purvamanyaya and pashimamanyaya tantras are still held as authority but practice is based on later tantras (12th century or after). For tantrists old does not necessarily become authorative. Because from traditional viewpoint all tantras originate from the mouth of shiva and thus necessarily authoratative. But scientifically, knowledge is not a stagnant pond water and new discoveries can be made in any area including spirituality. For present day tantrics Kularnava tantra is a very authoratative work.

Vaishnava agamas and tantras may have diverse roots since in some of the vedic element dominates while others have tantric elements. Vaikhansa system which is very much veda influenced and is now mostly lost is probably pre-tantric or at least not directly influenced. Pancharatra system which has tantric influence could be concurrent or inspired by the shaiva-shakta systems. At least Sanderson gives a quote somewhere to show they were influenced by shaiva agamas.