From http://leagueoflegends.wikia.com/wiki/Movement_speed, movement speed is calculated by:

Movement Speed = (Base Movement Speed + Flat Movement Bonuses) × (1 + Percentage Movement Bonuses) × Slow Ratio

E.g. if you have 310 base speed, your effective speed with both ghost (27% boost) and exhaust (40% slow) will be:

310 * 1.27 * 0.4 = 157.481

So no, the order they are applied does not matter; the end result is always the same. However, the slow will always be more effective.

From the example above, if exhaust wasn't applied, you'd gain 83.7 speed, however, when it is applied, you gain 33.48 speed.

Likewise, without ghost, the exhaust would subtract 124 speed, but with ghost, it subtracts 152.5.

No, the order doesn't matter, both the slow and boost will be applied. However, the slow will always be more effective, so it's not necessarily worth to pop ghost while exhausted.

From http://leagueoflegends.wikia.com/wiki/Movement_speed, movement speed is calculated by:

Movement Speed = (Base Movement Speed + Flat Movement Bonuses) × (1 + Percentage Movement Bonuses) × Slow Ratio

E.g. if you have 310 base speed, your effective speed with both ghost (27% boost) and exhaust (40% slow) will be:

310 * 1.27 * 0.6 = 236.2

So the order doesn't matter, the end result is always the same. However, the slow is always more effective, because it's a ratio of the effective speed with boosts.

From the example above, normally ghosting would give you 83.7 extra speed, however, if you ghost while exhausted, you gain only 50.2.

Likewise, being exhausted normally subtracts 124 speed, but being exhausted while ghosting would subtract 157.5.

Another example; if you slow and boost yourself by an equal amount, say 20%, the net effect would be that you're slowed:

310 * 1.2 * 0.8 = 297.6