There is a very useful analysis of a selection of multiple studies to be found here: http://www.strengthandconditioningresearch.com/exercises/squat/
I'll start out by assuming that you adjust your feet angle to your stance width (or vice-versa) to keep the femurs and tibias in the same plane as the line from mid-heel to mid-toe. I know this isn't exactly what you're asking — I'll get back to that later — but let's do so for a moment for the sake of discussion. Here's the effects of hip angle on various aspects according to the studies.
- EMG activity: greater for a wider stance compared to narrower stance.
- Quadriceps activity: no differences found for width variations.
- Hamstring activity: no differences found for width variations.
- Adductors (outward hip rotation): some conclusions that there's no difference for width variations, but contradicted in another study that concluded activity increased for wider angles, up to 30 degrees. Beyond 30 degrees no further difference was noted.
- Gastrocnemius and soleus (calf muscles): greater muscle activity in narrower stances compared to wider stances.
- Peak trunk angles: no difference between stances. (This would actually depend more on the location of the barbell on the back)
- Peak hip joint angles: same as for trunk angles.
- Peak knee joint angles: same again.
- Peak ankle joint angles: greater shank angles for narrower stances.
- Peak hip extensor moments: no differences between stance widths.
- Peak knee extensor moments: same.
- Peak ankle plantar flexor moments: no difference between narrow and medium but much greater for wide stances.
- External hip moment arms length: no differences, except at 45° knee flexion in the lowering and lifting phase, where it was greater for the medium and wide stance.
- External knee moment arms length: same as above.
- External ankle moment arms length: large negative length for wide stance, small negative length for medium stance, small positive length for narrow stance.
Now for the actual foot angle, rather than just stance width. The section for quadriceps mentions that with the feet turned out 20 to 30 degrees, compared to a neutral forward direction, there was no difference to be found in quadriceps activity. The same conclusions hold for hamstring activity.
both in Rippetoe's Starting Strength and (<- not sure) on Powerliftingtowin.com that a wider stance will result in smaller horizontal moment arms. See my crummy Paint image below.
If the black line is the barbell, kept over the middle of the feet, and the grey lines are the legs seen from above (narrow stance on the left, wide stance on the right) then the moment arms between bar and knees would be the green lines, and between bar and hips would be the blue lines. For a wide stance the horizontal moment arms are clearly shorter.
I'm actually critical of this assessment. I could be wrong, but I believe it to be a mistake to look at this horizontal moment arm, which would only play a role if one assumes the knee and hip joints remain perpendicular to the bar. They don't. I believe the actual moment arms are between the point where the bar's plane bisects the legs and the knee/hip joints, in which case the moment arms remain the same between stance widths. The studies discussed above seem to confirm this, but I might be misinterpreting something. It sort of stands to reason: if the moment arms were actually shortened, they would vanish with increasingly wide stances, to the point where, if the legs were almost parallel with the bar, there would barely be any. Obviously that's not gonna happen because otherwise we'd see people squatting standing like clowns. I'm thinking of asking about this, possibly here, or maybe on the physics SE.
So stance width notwithstanding, how would the foot angle affect anything? If you widen your stance and push your knees out during the squat, while keeping the toes pointed (more) forwards, you're introducing torque. In this case, at least where the ankles are concerned (but probably also the knees) the moment arm does operate at a different angle, closer to that perpendicular angle, because now your femurs and tibias aren't in the same plane anymore. So you're introducing another angle at the knee and ankle joints. According to Starting Strength this is in fact done by some advanced powerlifters, however it suggests you refrain from doing so if you're not in that category and know exactly what you're doing. I think that's solid advice.
So what does that mean for you? It's probably best to keep your femurs and tibias in the same plane, with the knees tracking over the toes, meaning your foot angle would mostly be a function of stance width. And you can do all the math you want, but in the end it'll be most effective to find out what works well for you. I myself notice that as I take a narrower stance, I can squat slightly more weight (or at least my work sets on less than 1RM feel easier) but my knees tend to come more forward and can end up hurting. Too wide seems to cost me some strength, and can lead to pain in my left hip, although it gives the knees a break. In the end I found my sweet spot with feet probably slightly below a 30° angle and ankles at shoulder width or slightly less. I'm not sure it lets me squat the most weight, but this way my hips and knees divide the load properly without either of them hurting afterwards.
EDIT: Just to clarify, I'm not claiming that moment arms between bar and knees/hips aren't important or won't vary, but I believe they'll vary only by bar placement on the back and the angles of the back, hip, knees and ankles during the movement. Not stance width.