I have Sheoldred, Whispering One and the Eldrazi Monument in play. At the beginning of my upkeep, I sacrifice a creature to pay the upkeep for the Monument. My plan was to bring it back out using Sheoldred's ability, but my opponent has a Scavenging Ooze. He taps one green and exiles the sacrificed creature when it hits the graveyard. Is he able to exile my creature after the sacrifice but before the Sheoldred ability activates?
If you sacrifice a creature to Eldrazi Monument's ability, you can't bring that creature back with Sheoldred during the same upkeep. But if you could, then your opponent would be able to stop you using Scavenging Ooze.
As your upkeep step starts, the first thing you do is put all abilities that trigger at the beginning of your upkeep on the stack. You can choose what order they are put on the stack, so you can have Eldrazi Monument's ability resolve before Sheoldred's ability. However, you also have to choose the target for Sheoldred's ability when it is put on the stack, so Sheoldred can only return a creature that was already in the graveyard before you sacrifice a creature to Eldrazi Monument.
It would work differently with a slightly different ability. Consider this ability:
At the beginning of your upkeep, return
targeta creature card from your graveyard to the battlefield.
In this case, the ability does not have a target, so you do not choose which creature to return until the ability resolves. Then the situation plays out like this:
You put the alternate Sheoldred ability and the Eldrazi Monument ability on the stack.
The Eldrazi Monument ability resolves, and you sacrifice a creature.
At this point, both you and your opponent have another chance to respond before the alternate Sheoldred ability resolves. Your opponent activates the Scavenging Ooze's ability targeting the creature you sacrificed.
The Scavenging Ooze's ability resolves, and the creature is exiled.
The alternate Sheoldred ability resolves, and you can return a creature from your graveyard to the battlefield. You can't return the creature you sacrificed, because it has been exiled, but you can choose a different creature, if there is one available.
There are 2 things going on here: 1) Your initial scenario doesn't work. 2) Your opponent would get to exile the creature after the sacrifice.
When Eldrazi Monument and Sheoldred both trigger, both abilities have to go on the stack. That means that there has to be a target in the graveyard for Sheoldred. So, a creature sacrificed to Monument won't be there to be targeted.
As for Scavenging Ooze, yes, the opponent can exile it in between triggers resolving. Triggers are just abilities on the stack. Players get priority before and after each ability resolves. Since they could activate Ooze, with their priority it could activate it. This is particularly relevant with cards like Emrakul, the Aeons Torn since it is in the graveyard while the shuffle trigger is on the stack.
It doesn't matter if your opponent has a Scavenging Ooze, you are not able to return the creature sacrificed to the Monument with Sheoldred on the same turn it was sacrificed.
This is because at the beginning of your upkeep everything that triggers goes on the stack at the same time. For the Monument this doesn't matter since you choose which creature to sacrifice when the ability resolves. For Sheoldred however since it has the word 'target' in the ability you have to choose a legal target when the ability is put onto the stack.
If we were to assume that Sheoldred's ability said 'return a creature card' rather than 'return target creature card' you still could not return the card because your opponent can activate abilities before her trigger would resolve, but after the Monument's would.
In order for any spell or ability to resolve each player must pass priority without doing anything, and if there are multiple spells or abilities on the stack priority must be passed by all players in between each spell/ability. There is no way to just 'resolve the stack' without all players getting to do things. In Magic priority is basically the system that allows players to do things, when you have priority you can cast a spell or activate an ability (and a few other things). Since your opponent gains priority in between the Monument's triggered ability and Sheoldred's triggered ability they have the opportunity to activate their Ooze's ability and remove the creature card from the graveyard before it could be returned.