In a speech, a lesson, or conversation, a tangent is a sudden shift in thought that seems almost unrelated to the rest of the talk. From NOAD:
figurative a completely different line of thought or action
So, in this case, an odd tangent would be the same as a peculiar aside. It's something that had the audience wondering, "Where is this coming from?"
This usage of the phrasal verb strike out is a bit trickier. Collins says:
strike out (v.) to start out or begin
So the phrase simply means he started talking praising China, and the audience (or this author, at least) didn't think that it fit too well with the rest of his speech.
I can see why you'd have trouble finding this if you Googled the whole phrase. The phasal verb strike out has other meanings, too, some of which are much more prominent, especially this time of year.