Having saw the sentence”needless to say”, I thought it was kind of leaving out, and the original form, in my guess, was like “(conjunction + it is) adjective(needless) to intransitive(say)”. Then I thought up sentences upon the abstract above, yet don’t know if they are correct or natural. I know whether they are depends, so please tell me if there is a context the sentences below fit naturally.
“Important to say” “Weird to say” “Strange to think”
Or are they just idioms to memorize?
Needless to say is a phrase, not a sentence, but you are right in thinking that it is short for It is needless (unnecessary) to say that.... A few phrases like that are well-established in the English language. Strange to say is one (not weird, because the use of that word in everyday language is modern). There's also wonderful to relate, mainly as a translation of the Latin mirabile dictu (wonderful here means remarkable, not very good).
I don't think you can use important to say on its own.
The phrase (not a sentence) "Needless to say" is a fixed phrase. See Are idioms not recommended in a formal situation? for more on fixed phrases.
It is short for
It is needless to say ...
or
It would be needless to say ...
or in still fuller form
It is (or would be) needless for me to say ...
It is a slightly odd phrase because the speaker or writer says that it is needless (not required) to say something, and then goes on to say it anyway. It is often used for emphasis. For example:
An hour into the date, I called Betty "June" by msitake. Betty and June had been funding for years. Needless to say I didn't get anywhere on that date.
The speaker wants to emphasize how obvious it would be that the date was a failure.
Another example:
Columbus thought that he could get to the spice and silk markets of India and China by sailing east across the Atlantic. Needless to say, North and South America were a significant obstacle to this plan.
The writer wants to emphasize ho much Columbus did not know about the state of the world.
“Weird to say” is not such a standard fixed phrase, and would sound odd to many fluent speakers. The same is true of "Important to say" That would be better rendered as "It is important for me to mention that..."
