Okay, since this is mostly for posterity anyway, here's what I've discovered:
The moves in question (from ECO C00/002) are:
1.e4 e6 2.c4 d5 3.exd5 exd5 4.d4 {- C01}
And if you go to ECO C01, just the table itself, not an individual line, you see this:
So you can reach the same position as the above movelist by playing the line listed in the second horizontal section plus the first move in variations 2-4 (in this case):
1.e4 e6 2.d4 d5 3.exd5 exd5 4.c4
So I guess that {- C01} is referring to C01/002-004, since White can't be at move 4 with that configuration except with those three lines.
This means that, barring any further (or initial) input, I'll just write those lines in, without their variations (since then I'd be writing out entire lines).
I can't figure out what this is supposed to mean. Does this refer to a transposition? If so, how do I write it out in the move list? I know that the dash, for Chess Informant, is supposed to mean "see". So it means 3...d5 see 2.f4. Does this mean that I then write out the line that follows from... From wherever d5 lands as a second half-move? Do I just ignore any moves that have already been made and fill in the list from there?
What about 8.Nf3 -- D20? This doesn't just lead me back to an earlier move in the movelist, from which theoretically I'd be filling in from there, it leads me to an entire ECO entry, which certainly has to have tons of lines that could match something like that???
I'm just really at a loss as to how to explain this particular notation, and I don't want to just include it as a comment, because it probably is shorthand for an entire sequence of moves.