We met somebody last night that was…

From an educational website:

We met somebody last night that did the speech therapy course two years after you.

In this sentence, the intended antecedent is "somebody", but an adverbial phrase sits between it and "that". Could "that" ambiguously refer to "night" instead of "somebody", since "night" is the word closest to "that"?

An example written by me:

We met somebody last night that was strange/unforgettable.

In my example sentence, could the adjective following "was" modify "last night" instead of "somebody"? How would native speakers interpret a sentence like this in both written and spoken English? Or is "last night" a fixed adverbial phrase that prevents "that" from referring to "night" at all?

While this seems possible grammatically, it would never give a sensible meaning and so the antecedent of the relative clause must be "somebody".

"Last night" is idiomatic. Note how it isn't used with a determiner ("the") and the meaning of of the phrase can't be fully understood by the usual meaning of "last". So "last night" should be treated in the same way as words like "tomorrow" or "yesterday".

It doesn't make much sense to modify "yesterday" or "last night" etc with a relative clause. There is only one "last night". So if the antecedent isn't "last night", it must be something else, and the only other sensible possibility is "somebody".

Now it might be possible to use a non-restrictive clause:

I met somebody last night, which was dark and windy.

It's a bit awkward, but I think the use of which (instead of who) and the fact that "dark and windy" is unlikely to refer to a person, nor the event of "meeting", would mean that this is understood to be a description of last night.

In your example

I met someone last night, which was strange.

The clause would probably be understood to act at the clause level, saying that "meeting somebody" was a strange event.

If "(the) last night" is not being used as the idiom, then modification by a relative clause is very natural.

I met him on the last night that he was in the country.

Here "last night" doesn't mean "yesterday evening", and can be modified with a restrictive clause.