Definition: unexpectedly; by surprise
Explanation: Used when talking about something that happened that you didn't expect.
Examples: All of a sudden, he became extremely angry. - We were having a nice talk, when, all of a sudden, she began to cry.
The word suddenly is an adverb that is defined as follows:
1 a : happening or coming unexpectedly <a sudden shower> b : changing angle or character all at once <a sudden drop in the ocean bottom>
2 : marked by or manifesting abruptness or haste <a sudden departure>
3 : made or brought about in a short time
As a general rule, the use of idioms is acceptable in casual discourse and interpersonal communication but should be avoided in academic and professional rhetoric.
I think the phrase you are looking for is "all of a sudden," not "all on a sudden."
This phrase has the exact same meaning as "suddenly."
The word sudden is an adjective that means happening or coming unexpectedly. "A sudden drop in cabin pressure," or "A sudden thunderstorm." Suddenly is the adverb of that adjective. "Suddenly, the cabin pressure dropped," or "Suddenly, a thunderstorm came up out of nowhere."
To insert the phrase "all of a sudden" is more of a vernacular use or an idiom of the word "suddenly." It is more figurative and therefore less formal. Obviously in writing, it is muddier - but when spoken, it sounds more conversational and familiar. Americans tend to use "suddenly" in writing as it is more formal and "all of a sudden" in speech for the opposite reason.
Structurally they are similar, there are lots of words put together or arranged differently still convey the same meaning in the end.