Is there a way to see the level of the players who join my game or whom I join the game of? I feel like there was only ever one person who could tell what level I was, but I didn't get the chance to ask them how they knew.
There isn't, not directly.
However, if you turned off local monster scaling, you can tell approximately what level the host is based on the enemy levels, because the monsters will be scaled to the host.
To see the level of other players, look at the PLAYERS tab of the character menu.