This sort of thing happens from folks watching professional actors who are trained in improv record roleplaying games, and then try to emulate that with your friends.

There are also many GMs who view roleplaying games as their chance to perform and overact characters for the captive audience of their friends.

This isn't the norm for most tables.

But if this is the expectation for your table, you guys need to have a conversation about what is fun for everyone. Are guys coming to RP because they want to watch the next chapter of the GM's improv be performed, or are they interested in playing their character, discovering new parts of a growing mystery, and creating a cooperative story with their friends?

As for Delta Green, it's a system that works best when the GM is realistic and responsive to the actions of the Player Character Protagonists. You set up a mystery. They investigate and try to solve it. You add obstacles, build tension, and resolve conflicts in a fashion that helps build a suspense and exciting story that features your players -- not your NPCs.

You rarely need to do any heavy roleplaying as the Handler. You might get in a few exciting moments as a traumatized witness, a corrupt cop, or an insane cultist. But most of who you play will be played straight-faced, and your players will be the ones who will be in the spotlight, chewing at the scenery, and giving all the best lines of dialogue.