Your opponent will not get to sacrifice Ordeal of Nylea or search for lands.
Although an ability does still resolve if the source leaves the battlefield, in this case, that ability resolving will not cause all of its effects to happen.
The triggers from Ordeal of Nylea will still resolve even though the source has left the battlefield.
112.7a Once activated or triggered, an ability exists on the stack independently of its source. Destruction or removal of the source after that time won’t affect the ability.
So you will still follow the instructions on the ability:
put a +1/+1 counter on it [the creature that attacked].
This instruction will not do anything because the creature is not on the battlefield anymore.
You will then go to the next instruction:
Then if it has three or more +1/+1 counters on it, sacrifice Ordeal of Nylea.
This will check how many counters were on it when it was last on the battlefield, which is only 2, so it won't pass the check.
608.2g If an effect requires information from the game (such as the number of creatures on the battlefield), the answer is determined only once, when the effect is applied. If the effect requires information from a specific object, including the source of the ability itself, the effect uses the current information of that object if it’s in the public zone it was expected to be in; if it's no longer in that zone, or if the effect has moved it from a public zone to a hidden zone, the effect uses the object’s last known information.
Even if all that weren't the case, your opponent would be unable to sacrifice Ordeal of Nylea because it is already in the graveyard by the time they are instructed to do so.