Paris Jackson -- The Nanny Would Sneak Into Michael Jackson's Bed

Paris Jackson told a creepy story about one of her former nannies and Michael Jackson ending up in bed together ... and she said it under oath during a deposition taken for the wrongful death suit against AEG.

Video of Paris' deposition was played in court Tuesday ... and the highlight was her description of Michael's relationship with ex-nanny Grace Rwaramba.

In the depo ... Paris explained to attorneys for AEG that Michael warned his children about Grace, telling them ... "She was sneaky. She wasn't an honest person, and she lied a lot."

Paris said she didn't know specifically what she lied about -- but then seemed to suddenly remember one freaky detail about Grace sneaking into Michael's bed while they were staying in hotels.

Paris starts out saying ... "This is gonna freak you out."