It wont move but its still inside of the monster. So the monster moves its going to move with the monster, I dont see the point in that one. Atleast thats how I would see it.
Immovable rods are stationary relative to the
planet not to their holder. You leave the rod in the monster's stomach, it stays stationary, pinning the monster in space by its guts. Pretty nasty move.
Some other uses:
Affix a siege crossbow (or similarly retarded weapon) to it on a pintle mount. Use it as a portable steady firing position
Activate it inside of a Bag of Holding. Attempt to move the bag. Ask the GM what happens
Tie activation to a command word and use it to support thousands of tons of rocks, or the party, as part of an elaborate trap
Build a skyhook using the rod as a foundation
Support a skyscraper from the top and bottom
Emergency Brakes
Weld it into a warforged: use it as a restraining bolt
Weld it onto a slave collar: See above
Combine with Acrobatics: freerun to infinity
Block a sturdy door
Use two as an infinite ladder you can climb with your hands
Attach it to a shield and activate it when you think you're gonna get hit.
Drop one inside a boat you don't like before they leave port
If being chased in a carriage, lean down behind your carriage and activate the rod in midair (for bonus points, make it invisible)
Use it as a weapon hilt: Create the Sword in the Stone