The MAIN difference that I'm seeing immediately is mostly tense changes. "Would" is the past tense of the verb "will" and "Could" is the past tense of the verb "can." As for may be and might be, I think this link should help you with that.
"Either" is an affirmative adjective. It has many functions, including following a clause after a negative statement: "It's not my horse, but it's not her horse either." "Either" is also used in conjunction with (or substituted by) "or." For example: "You may have either the apple or the orange." Or "You may have the apple or the orange."
Neither (which pairs with "nor"), on the other hand, is the negative form of either and "or", and usually used as a conjunction to negate two phrases. For example: "I don't want the apple nor the orange!" Or, "I want neither the apple nor the orange!" Or, "That's neither here nor there."