So my users are complaining that they're getting spam ads opening up full screen when they click into new threads

It happened to me once the other day whilst I was on my mobile but I didn't get too worried as couldn't replicate but now it seems it's happening often to many users.

Any ideas on how to quickly eradicate this?

Probably rogue ads. I would look there first. 
In theory, your site could also be hacked and the malicious code is delivered from your site directly. 

Just now, opentype said:

Probably rogue ads. I would look there first. 
In theory, your site could also be hacked and the malicious code is delivered from your site directly. 

 

I use an ad agency so don't think it's rogue ads - I think it's malicious code (gut feeling?)

https://sitecheck.sucuri.net/