How should I describe something that will very likely happen right away? For example, would it be it correct to say, "It is about to rain"?
Certainly. You can say "It is about to rain" like you said. Depending on the context, you could also say:
(However, this question is a little vague. More detail about context would help.)
A single word would be :
It is also correct the way you stated it, "It is about to..."
Just to make a distinction, "It is about to..." is best used for verbs, i.e. "rain", or "snow" or "melt". "It is about to melt."
"Imminent" is used with nouns e.g. "death", or "decision", or "arrival". "Uncle Fred's arrival is imminent."