Many punctures on my 18" wheels Strida
That is an unusual tire size, and it's true you don't have a lot of options. 


As Ross points out, Schwalbe does make the Marathon tire (which is very robust) in that size.
You could keep your current tires and put some tire-liner strips inside them. You'd need to cut them to fit.
You could add sealant to your innertubes (you might need to swap tubes). This won't prevent the punctures, it would just mean they're less trouble.


Good luck.