Strange search spam on wordpress?

It’s almost certainly from a bot. Whether it’s “spam” or not depends on how you define spam. If spam is a type of illicit advertising, then spam is not what this is. It’s more likely a vulnerability probe that’s looking for a specific response that would indicate a weakness that can be exploited. If such requests just result in a typical nothing found page, there’s no reason for concern. If there are so many such requests that it’s skewing your analytics data there are ways of filtering them out.

What is redirecting to those links? Why in a pop up/under? I’d say your issue then is with whatever it is that’s doing this.

Sorry, I don’t have any suggestions. I don’t consider them to be part of a proper user experience, so never had a need for such a script. It seems like the script you had was OK except it requested the wrong URL. It might not be too difficult to fix that aspect. But fixing errant scripts isn’t for everyone.