Well, it could be really wild. Maybe Steven could use his gem powers to try and stop Zim's crazy plans for world domination. Zim, on the other hand, would probably be super confused by Steven's powers and the whole concept of gems.
I think Steven and Zim would be the most interesting pair. Steven's kind - hearted and positive nature contrasted with Zim's evil and self - centered personality would create a lot of comical and tense moments.
One possible plot could be that Zim and Dib from 'Invader Zim' somehow end up in the 'Futurama' universe. Zim might see the advanced technology in Futurama as a new opportunity to take over a planet. He could mistake Planet Express for a major power center and try to infiltrate it. Dib, on the other hand, would be excited to explore this new world and might team up with Fry, Leela, and Bender to stop Zim's new evil plan.
One idea could be a crossover with 'The Simpsons'. Zim could try to infiltrate Springfield, thinking it's a key Earth location for his invasion plans. Maybe he mistakes Homer for a powerful Earth leader and tries all sorts of wacky schemes to take over the town through him.
One interesting Gir crossover Invader Zim fanfiction could be one where Gir teams up with Dib to stop some new alien threat that neither Zim nor the other regular villains can handle. In this story, Gir's unpredictable and silly nature might add a lot of comical elements to the usually tense relationship between Dib and Zim.
The clash of different aesthetics. Jhonen Vasquez has a very distinct style in both JTHM and Invader Zim. When you cross them over, you get a really unique visual and narrative blend.
Often, there's a theme of self - discovery. As Female Zim is a different take on the character, she might be on a journey to figure out who she is in this new form. Also, the theme of adaptation is common. Just like in the original where Zim has to adapt to Earth, Female Zim may have her own unique ways of adapting, whether it's to Earth's environment or to the reactions of the other characters around her. And there's also the theme of power. How does being female change Zim's perception and use of power? This is something that many fanfictions like to play with.
In a crossover with 'Powerpuff Girls', the Professor could be an interesting character to include. He might study Zim's technology and try to find a way to use it for good, while the Powerpuff Girls are busy fighting Zim's minions. And Zim would be both fascinated and enraged by the super - powered girls.
Definitely Dib and Dipper. They are both curious and into the strange and supernatural. Dib with his alien - hunting skills and Dipper with his knowledge of the Gravity Falls mysteries would make a great pair.