You cannot use the Tentacle Rod as it requires an action to activate
The "Use an Object" section of the PHB states:
When an object requires your action for its use, you take the Use an Object action.1
Thus, activating the Tentacle Rod requires your action and opportunity attacks do not allow you to take actions, only reactions.
This is similar to the fact that you cannot grapple/shove as an opportunity attack because they require the Attack action, which you cannot make with an opportunity attack. The Sage Advice Compendium explains this as follows:
Q. Can an opportunity attack be used to make a grapple or a shove?
A. Grappling and shoving are special melee attacks that require the Attack action (PH, 195). An opportunity attack is a special reaction. Take the Ready action if you want to attempt a grapple or a shove as a reaction.
1 The DMG (page 141) clarifies this further:
If an item requires an action to activate, that action isn't a function of the Use an Object action, so a feature such as the rogue's Fast Hands can't be used to activate the item.
Using the Tentacle Rod does still require your action, but it specifically is not the Use An Object action. This would be the Activate An Item action or perhaps the Tentacle Rod action.