JK wrote:

Okay. I'm lost. Each switch has three wires: Red, Black, and White. The
receptacle has three as well (red, black, and white). On the receptacle, the
red is attached to a brass screw, as is the black, with the white on the
opposite silver screw from the black. And I undid the hot tab. One of the
plugs is not tied to a switch; that is, it's always on. The plug with the
red is tied to the switches.

On the switches, the red wire is attached to the colored screw (the one that
is not copper, I believe it's labeled "common"), and the white and black are
connected to the other screws.

Truly bizarre. The outlet (plug) that's always on is powered directly
from the AC line. Questions:

1. Is the black wire going to that outlet's brass screw also spliced
with another wire? (This could be with a wire nut or via a wire poked
into a hole in the back of the outlet.)
2. What color is that wire? (Tell me it's red.)
3. How many cables attach to the outlet box?
4. How many wires in each cable? (Don't count the bare wire.)
5. Are there any other splices in the outlet box? How many wires, what
colors?
6. Does each switch have only one cable to it? If not, how many cables
and how many wire in each?

The only way I can see for this to work is as follows:

The black wire going to the always-on outlet is also spliced to a red
wire that goes to the common terminal of one switch. The common terminal
of the other switch has a red wire that goes to the brass screw on the
switched outlet. The other two terminals on each switch are connected to
each other with black and white wires.

Schematically, this will work. The strange part is the actual cabling.
There must be lots of splices in the outlet box.