"etc." is very informal, so should only be used in a suitable situation. It is less often used in oral English, but when it is, it is obviously pronounced fully as 'etcetera'. "and so on" would be more often used orally, and would be used in situations where you are trying to explain a sequence, such as "the squares: 1,4,9,16, and so on". "and the like" is a somewhat less informal expression. That would be when you are listing things that are similar. Another alternatives would be "and so forth" If you were listing items, you could say "and other examples" or "and similar examples"

"And the like" is usually used after only one item in a sentence: "Teachers and the like are not welcome on this playground" "And so on" is usually used after a list of items and stresses that the omitted can be known simply by thinking about it. ("And so on" as in "and you already know how this list goes on") "We went fishing, scuba-diving and so on." "I went to a Christmas party with Mary, Joseph, Joshua and so on." "Etc" is short for "Et Cetera" which comes from latin and means "and other things". It is a little more formal and hardly ever used in spoken English, while it means pretty much the same as "and so on." A friend of mine always said "yada, yada, yada" to express the same meaning. According to wikipedia it comes from a TV Show called "Seinfeld", not sure if that's where she picked it up.