Hard question.
Rahnesha gives a great example in my opinion.
Sometimes they can all be used interchangeably, other times not. Consent is probably used more when you are giving someone a right to something personal. You give a doctor consent to operate on you, (it’s true that you also permit the doctor to operate on you, or agree that the doctor can operate on you but consent is more appropriate), the age of consent is another example, or you might give a lawyer consent to act on your behalf.
So the way I look at it, if you agree, or permit to give something personal to someone else (your legal rights, your body) you consent to it.
Permission is also something that you give. If you want to borrow something from me, I’ll need to give you permission, or permit you to borrow it. I can ”consent” to let you use my lawnmower, but permit is probably a better term.
Agree is a much broader term. It can apply to the examples above, but I don’t necessarily have to give something up to “agree”. I usually do have to give something up If I permit or consent. For example I agree that Ranesha has given a good answer, Ive lost nothing by saying that. If I permit you to use my lawnmower, then I give you my lawnmower for a couple of hours (and I don’t have it). If I consent to an operation, I allow a surgeon to cut me open.
Hope that hasn’t confused you further, also just my opinion.