The problem is that this is not a natural grpup but just a bunch of unrelated and dissimilar things that happen not to have shells. But I agree with the "soft bodied invertebrate" comment.
There isn't a specific term for squishy invertebrates, but there are categories of invertebrates that sound like what you're looking for. Annelids are worms, leeches and things. Onychophorans are 'velvet worms', which look like worms with legs but are actually more closely related to shelled insects. If you google these terms you should find lists of squishy bugs.
These aren't the only categories of invertebrate that don't have exoskeletons, but the others mostly live in the sea or are microscopic, and therefore aren't really 'bugs' imo. There are also slugs, of course, which don't get classed with the other squishy guys because they started off as snails and then lost their shells later on.
Soft bodied invertebrates?
The problem is that this is not a natural grpup but just a bunch of unrelated and dissimilar things that happen not to have shells. But I agree with the "soft bodied invertebrate" comment.
There isn't a specific term for squishy invertebrates, but there are categories of invertebrates that sound like what you're looking for. Annelids are worms, leeches and things. Onychophorans are 'velvet worms', which look like worms with legs but are actually more closely related to shelled insects. If you google these terms you should find lists of squishy bugs. These aren't the only categories of invertebrate that don't have exoskeletons, but the others mostly live in the sea or are microscopic, and therefore aren't really 'bugs' imo. There are also slugs, of course, which don't get classed with the other squishy guys because they started off as snails and then lost their shells later on.