Learn English – what’s the meaning of “take me off the speaker”

Though the complex preposition of off of is widely used, one may argue that it's redundant.

Here is the Oxford Dictionaries' reference:

Off of is often used in place of the preposition off in contexts such as she picked it up off of the floor (compared with she picked it up off the floor ). Although off of is recorded from the 16th century (it was used by Shakespeare) and is logically parallel to the standard out of, it is regarded as incorrect in standard modern English.

Now, about the point

someone got a point - someone got an idea to think upon

See Merriam-Webster's definition 4a: "a course of conduct, action, or thought; especially : an official or public position", as in the party line. So take the line that X means something like to adopt X as an official position or stance on an issue.

Your suggestion of have the view that is approximately right, but I think take the line is a little more forceful. It suggests that this is their view, but it also suggests that they believe it very firmly, might try to convince other people of it, and might take action based on it.