Either way usually refers to two scenarios, but it is not a rule. For example Michael or John might not make it, either way we are finishing the project. When you use anyway it can also have a meaning to get back to the original topic of conversation. To conclude, they can be used as synonyms, but most of the time it would depend on the context of the conversation which one you would use.

"Anyways" should never be used, although you may hear it. "Either ways" is incorrect and I have never before heard it. "Anyway" is commonly used in conversation at the start of a sentence to dismiss a digression, preferably, in my mind, one's own digression. ("Anyway, I'm sorry, what were you saying?") Here in America it has been increasingly used, and overused, in a joking or rude manner to indicate that another person's comments are inappropriate or beside the point. ("Anyway, as I was saying before I was interrupted...") Aside from its being a conversational tic, you could use it in the following way: "Although the odds were against me, I decided to try it anyway." "Either way" implies there are two options. For example: "Should we wash the dishes before we go or after we get back?" "Either way is okay with me."

Hi, in British English, we would only use "Anyway" - eg "Anyway, let's start this next week". I would never use "Either way", "Either ways" or "Anyways". This may be different in American English. I hope this helps :-)

Either way is used if you are referring to two or more choices. The correct usage of anyway is “you can do this the right way or or you can do this anyway that you choose .”