For possibility:
* Could: "She could be right."
* May: "It may rain tomorrow."
* Perhaps: "Perhaps we should go home."
* Possibly: "It's possibly the best solution."
* Potentially: "This potentially dangerous situation needs to be addressed."
* Maybe: "Maybe we'll see you later."
For strength or power:
* Power: "The king wielded great power."
* Strength: "The team showed incredible strength."
* Force: "The force of the storm was incredible."
* Capacity: "She has the capacity to lead."
* Ability: "He has the ability to succeed."
* Capability: "They have the capability to complete the project."
For permission or likelihood:
* Can: "You can borrow my book." (permission)
* Likely: "It's likely to rain today."
* Probably: "I probably won't be home before 9pm."
* Possibly: "It's possibly the best solution."
The best word to use will depend on the specific context and meaning you wish to convey.