Brown, 37, has made appearances in the Premier League for five different clubs, while Jennings played for Motherwell in the Scottish Premier League.
O'Connor, 26, was released by Rotherham United this summer despite helping the club win promotion to the Championship last season.
Vale manager Micky Adams told reporters: "We're delighted to bring both to Vale, they're two vastly experienced players.
"The club have created some good competition for the midfield places and I'm excited about the coming season."
The three new signings were announced on the same day as the club insisted thst football operations would not be affected by a winding-up petition over an unpaid tax bill.