Olivia Wilde, Jason Sudeikis Says Ex-Nanny's Claims About Them Are Untrue

The former nanny to Olivia Wilde and Jason Sudeikis' kids claims they were nothing but toxic to each other, and listed off alleged reasons why ... but Jason and Olivia say she's telling nothing but lies.

Reports started flying Monday after the ex-nanny told DailyMail the alleged drama ... including how Olivia apparently left Jason for Harry Styles. She also said the two would get into explosive fights -- claiming Jason laid in front of Olivia's car once to prevent her from leaving to go see Harry.

The nanny also claimed Jason once got very upset when Olivia made her "special salad dressing" for Harry.

Olivia and Jason are calling BS, though -- telling TMZ ... "As parents, it is incredibly upsetting to learn that a former nanny of our two young children would choose to make such false and scurrilous accusations about us publicly."

They go on to call their former nanny's claims an "18 month long campaign of harassing us, as well as loved ones, close friends and colleagues" ... something they say they've reached their limit with.

OW and JS tell us they'll continue to focus on raising and protecting their kids ... "with the sincere hope that she will now choose to leave our family alone."

As for Harry and Olivia, all seems well ... we got shots of them grabbing dinner in NYC just a few weeks ago, and she's been spotted at his shows.