I am trying out for Magic of Orlando this year. I am wondering how to mark time in time signatures such as 7/8, 11/8, 9/16, and such. Thank you.

Usually the time will be broken down into groups of 2 and or 3 eighth notes. Then some foot of yours will hit the ground every time one of those groupings passes you by....
e.g. in 7/8, a common subdivision is 2+2+3. If I were marking time, I would say "Ta ge Ta ge Ta ge da, Ta ge Ta ge Ta ge da, etc...".and every time my mouth said "Ta" I would step on the ground. 11/8 has a bunch of different groupings, but two common ones I've seen are 2+2+2+2+3, and 4+3+4 .

For some reason, when I look at 9/16, I keep thinking 3/4, even though it's clearly not, haha.

At my old school, 7/8 (and 11/8 probably), we marched the quarter note downbeat.
Basically, each 8th note beat is (in 7/8, step is when the foot hits the ground and cross is when the ankle bones cross)
step cross step cross step cross step

and then the next measure
cross step cross step cross step cross

and so on and so forth. This is equivalent to 7 steps. If you're wondering how to count it, you could do it the way above
12 12 123 || 12 12 123
But you'll notice that in the 2nd measure, your foot will be stepping on the offbeats. I like to count 7/8 measures as
12 12 123 || 456 12 12
This way, in the 1st measure, your foot steps on the downbeats and in the 2nd measure, the first step is on a downbeat as well.

Some people will have you march it straight I hear.

The first portion of our show this year was in 7/4, but we marched it very oddly: ONE two three four FIVE SIX SEVEN (where caps are beats on which we actually changed feet). I don't suspect they'll do that in upper-tier (or even any) drum corps. I usually just think of it as 1 2 3 4 | 1 2 3, if it's practical. I'm going to try subdividing per EnigmaticRonin's description; it'd be fun to try, anyway.