How can I plug the gap between a dishwasher and kitchen skirting board?
It's not the interior holes you need to deal with...it's the external ones. They're getting in the house somewhere/somehow and that's what you need to block.

The simplest way to do that is find the holes, and stuff them with stainless steel wool. The rodents will not want to chew through that. 

Plugging the interior holes/gaps won't do much. They'll just eventually chew a new hole elsewhere.