If your Odey senses were tingling at a trampoline park in NJ this weekend ... it's because #13 was there in a full Spider-Man costume -- and the story is pretty great! 

The NY Giants superstar caught wind that his teammate, Jonathan Casillas, was throwing a party for his 6-year-old daughter, Jade, who happens to be a big Odell Beckham fan.

We're told Odell wanted to surprise Jade -- so he got a black Spider-Man costume (with a full mask covering his face) and kicked it with the kids ... who had no idea Spidey was really a huge NFL star.

Odell eventually unmasked himself and the video is awesome. We're told Jade (and her mom) loved the surprise ... they had no idea!

As for the costume ... we debated if it was actually a Venom suit but ultimately decided it was more like the black Spidey suit from "Spider-Man 3."

Venom doesn't typically have webs on the suit.

Yeah, we're dorks. Whatever.