Asu? Ashita?

Are there any actual difference between あす and あした?

"Ashita" is slightly more colloquial than "asu." I think the NHK (national broadcasting company) weatherman - somewhat in an official tone - says "asu no tenki" referring to "weather for tomorrow" :) But both are used almost interchangeably.

明日 (tomorrow) can be read みょうにち / あす / あした.

みょうにち is so formal that there may be examples where it can not be replaced by あす or あした.

Between あす and あした, あす is more formal, あした is a little more colloquial.
(あした meant "morning after the end of night" in old Japanese, then got to mean "tomorrow" and became colloquial.)
These two are almost interchangeable, with exceptions such as idiomatic phrases.

Newscasters and weather forecasters mainly use あす for tomorrow, in news show programs by major broadcasters such as NHK (Japan Broadcasting Corporation; sorry, it's not a national company).

Both あす and あした can be used to represent near / coming future. e.g. 日本のあすを考える: think of Japan in the coming future. みょうにち is not used in this way.

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Thanks AK and omotenashi for the detailed explanations. :)