Can one creature or character use both an immediate interrupt and an opportunity attack in the same round, or are they mutually exclusive actions?
Yes. They can be performed during the same round and during the same turn.
An Opportunity Attack is defined as:
OPPORTUNITY ATTACK: OPPORTUNITY ACTION
One per Combatant’s Turn: You can take only one opportunity action during another combatant’s turn, but you can take any number during a round.
Interrupts Target’s Action: An opportunity action takes place before the target finishes its action. After the opportunity attack, the creature resumes its action. If the target is reduced to 0 hit points or fewer by the opportunity attack, it can’t finish its action because it’s dead or dying.
Thus an opportunity attack is an opportunity action which occurs once per enemy turn and interrupts their action on their turn.
This definition is reinforced by Opportunity Action:
Once per Combatant’s Turn: You can take no more than one opportunity action on each other combatant’s turn. You can’t take an opportunity action on your own turn.
Interrupts Action: An opportunity action interrupts the action that triggered it.
Despite using the term "interrupts" it is no-where classified as an Immediate Action:
Immediate Action Trigger: Each immediate action—usually a power—defines its specific trigger. The one type of immediate action that every combatant can take is a readied action.
Once per Round: You can take only one immediate action per round, either an immediate interrupt or an immediate reaction. If you take an immediate action, you can’t take another one until the start of your next turn, but you can’t take an immediate action on your own turn.
While there are two types of immediate action (immediate interrupt and immediate reaction) they are both triggered off the immediate action definition, rather than the opportunity action. As these two sub-types of actions (immedite interrupts versus opportunity attacks) are based on different actional definitions that restrict by rounds for IIs and turns for OAs, they're different and may be taken in the same round. If they happen from the same action, there is no clear ruling as what triggers first, and so it is by the choice of the person taking both actions. II triggers tend to be very precise, however, and will usually resolve the issue if read carefully.
The most pragmatic example is that of a spellcaster next to a warden. The caster provokes by casting a ranged attack at a different target, as well as violating the mark.
Warden's fury triggers on:
Immediate Interrupt Melee weapon
Trigger: An enemy marked by you makes an attack that does not include you as a target
Whereas the OA triggers on:
Ranged and Area Powers Provoke: If an enemy adjacent to you uses a ranged power or an area power, you can make an opportunity attack against that enemy.
As, pedantically speaking, the decision to use a power occurs before the targeting of the power, the warden would first resolve her OA, and would then resolve her II, severely castigating the artillery for being so foolish as to not shift first.