I suppose it depends on how you define Unorthodox... Is it based on popularity? Is it based on how many of the conventional rules (wisdom) that opening violates? Somewhere in between?
Unorthodox or Not?

I think the list would be endless. In his book Schiller includes variations of well know and established openings in his list. For example: the Advance Variation of the Caro-Kann. The Caro-Kann is not unorthodox and the Advance Variation might be a bit unusual but it's played enough to be included in books on the C-K. So is the Advance Variation unorthodox? Not in my book. It's a question of the definition of "unorthodox" and also the definition of what distinguishes one opening from another. The Nimzo-Larsen Attack is considered unorthodox by most people but not by me 'cause I play it all time.
As a group, particularly in vote games, I think we should explore some of the most unusual in order to live up to our name.

Yeah, true enough. We'd get into discussions over semantics if we started including every oddball variation of mainstream openings. For example, my newest curiosity is this...
1. e4 e5 2. Nf3 Nc6 3. Bb5 a5 (instead of ...a6)
It's odd but is it unorthodox? LOL

Both Marshall and Morphy played the Danish Gambit with success. It is NOT listed in Eric Shiller's compendium, UNORTHODOX CHESS OPENINGS.

"Below master level, all openings are sound." ---William Lombardy
Maybe it's not a matter of what is unorthodox and what is not, but as a group I think it's more of an indication of the types of players we are; fearless, willing to experiment and follow the road(s) less traveled. Someone once said that the lifeblood of chess is speculative attack.
I know somebody asked in the Notes whether the Danish Gambit would be deemed unorthodox. My immediate answer is no, only because it has some following and still gets mentioned in most opening manuals.
But I'm curious what else is considered unorthodox? I have Schiller's book and I'd even question whether the Latvian Gambit belongs in there.
Perhaps we should consider compiling a list, although it might be too lengthy.