Tanker developer here. We use libsodium as our underlying cryptographic library. It uses XChacha20/Poly1305 for symmetric encryption, Curve25519 for asymmetric encryption and signature, and Blake2 for hashing.
TweetNaCl is roughly equivalent to libsodium, on which Tanker builds. Tanker is easier to integrate into your app because it takes care of key sharing, multi-devices, user group managment, etc. These are all things you would have to handle by yourself using just a cryptographic library like TweetNaCl.