Harangue and rant can be used as either a noun or a verb, but tirade can only be used as a noun.
Harangue as a noun is a lengthy and aggressive speech given to an audience of some sort. Harangue as a verb is lengthy and aggressive speech directed at someone or some group in particular.
Rant as a noun is interchangeable with tirade. Rant as a verb is somewhat different than harangue because it isn't directed at anyone. When you rant, you're making a lengthy, angry speech to anyone within earshot. Tirade and rant can be used to describe angry writing, and I associate harangue with angry speech only (AmE).
A tirade can only be a noun, and is more commonly used than harangue. It is very close to both a rant and a harangue, but it doesn't have the sense of being addressed to an audience like a harangue does, nor the sense of not being directed to any particular audience that rant does.
Whenever she watched cable news, she would rant about the lack of standards in modern journalism. These rants could last for an hour.
Whenever she watched cable news, her tirade on the lack of standards in modern journalism would last for an hour.
Whenever she watched cable news, she would harangue us about the lack of standards in modern journalism. The only way to end her harangue was to turn off the TV.