One of the definitions for every found in the New Oxford American Dictionary is:
(used for emphasis) all possible; the utmost : you have every reason to be disappointed.
So, the speaker is implying that there is more than one way to annoy someone, and these people will find all of those ways to do that. Essentially, the speaker could have also said:
Especially when they find all the imaginable ways to annoy or pester you.
When every is used like this, it’s generally hyperbole. Insofar as I know, no one keeps a list of all the ways a person could annoy you, and, even if such a list did exist, I doubt the speaker would have checked each entry before deciding to use the word every. Therefore, each of these conveys pretty much the same meaning, although the top two read a little more strongly and emotionally, and the bottom one is a bit informal:
- They will find every way imaginable to bother you.
- They will find every way under the sun to bother you.
- They will find a myriad of ways to bother you.
- They will find all sorts of ways to bother you.
- They will find a ton of ways to bother you.
As for whether or not all these ways are used one-by-one over time or all at once, that’s pretty much left up to the imagination of the listener. The phrase itself doesn’t imply one over the other.