Consolidation is a FAA requirement to get 100 hours flight time within 120 days of your checkride. If you don't complete the consolidation requirement you go back to the training center for refresher training. The airline may be approved to extend the 120 days to 150 if a check airman observes your flying and says you're still good.

Displacement could be being pushed out of your seat, your aircraft or your base. Usually the union contract will say how it's done. When times are good people can move up to bigger equipment and the left seat Displacement occurs when times are bad and people are forced back to the right seat or to a less senior aircraft. It may also occur if a crew base is reduced or shut down and senior crew members push junior pilots to another base.

IOE is really just OE now but it's Initial Operating Experience. After you complete training on an aircraft you get a babysitter, a Line Check Airman. How long depends on what kind of training you complete which is why initial got dropped from the terminology. You could fly a plane for years as an F/O and if you upgrade you have to complete another round of OE before you are turned loose as a Captain.