"Avenue" is a more formal word, and has a more focused definition than 'ways" or "method" . Websters dictionary defines 'avenue' as a channel for pursuing a desired object avenues of communication so an avenue for attracting customers -- attracting customers is the desired object (what you want) and the channel to do it is the internet. From Cambridge': a method or way of doing something; a possibility: China and the United States are exploring avenues of military cooperation. Only two avenues are open to us – accept his offer or file a lawsuit. You would not replace "avenue(s)" with 'way(s)' in any of the above examples.

First, “Avenue” and “Way” are words used to designate roads. In my area, “avenue” (and “street”) are common; “way” is rare. But my guess is that depends on what country you’re in. Otherwise, “avenue” isn’t as much a general method but focuses a little more on the result. “Way” is a common word often used with a possessive article. His way of learning English seems to be working well. Grandma calls her way of cooking turkey “the high heat method”. I love the way he lives life - he’s so positive. How do I love thee? Let me count the ways. (Line in a famous sonnet) It’s my way or the highway. (Expression meaning “do things as I want you to, or go away”) (Not “avenue” in any of the examples.) Rena gave some examples where “avenue” is better than “way” but I don’t think “way” would sound too wrong, just less formal and precise.

@Joa Yu Thank you

There is no difference in the example you gave and I don't think there is a difference in general either. There are however certain instances where using "avenue" instead of "way" is bizarre - e.g. "I want to know the best way to make this cake." is used but not "I want to know the best avenue to make this cake."