Jason Sudeikis Thanks Kids at Emmys Amid Custody War with Olivia Wilde

Jason Sudeikis thanked his kids at the Emmys -- reminding folks he's in a nasty custody battle with Olivia Wilde, perhaps unintentionally.

The actor was delivering an acceptance speech Monday after his show, "Ted Lasso," won for Outstanding Comedy Series ... and toward the end, he name-dropped his young son and daughter, Otis and Daisy.

It sorta flew under the radar, as not everyone knows his children's names by heart -- but it was there ... and if you've been following along, it may run deeper than a simple shout-out.

As you know, both Jason and Olivia have been at war lately over where their kids should live, and how much time they spend with each parent -- a case that's not yet settled, but which has had a lot of bumps along the way ... including a public serving of documents earlier this year.

A process server, acting on Jason's behalf, dropped legal docs at Olivia's feet while she was presenting for her new movie at CinemaCon -- something she later called "vicious."

JS denied having planned it to happen that way deliberately, but OW thinks otherwise. In the end, Olivia walked away with a win ... getting a judge to side with her that their custody case should be heard in L.A. and not New York, which is where Jason wanted to hash things out.

None of that drama was on display, though, when Jason was speaking ... he was all smiles with his cast onstage, and didn't further allude to the fight with Olivia whatsoever. Although, he might have been wondering if he was about to get served.

BTW ... Jason took his good vibes and carried them on outside the venue. We ran into him on the street after the show, and the dude was totally engaging with fans ... snapping selfies and signing a ton of autographs. He even gave 'em some life advice.