Some species are native, many are introduced and naturalized. Many more are not naturalized and not listed on the 'approved' list of isopods that USDA gives out easy permits for (I'm permitted for shipment to many states, though not to FL since their requirements are quite a bit more stringent). Here's the 'approved' list that is relatively straightforward to get permits for:
Armadillidium klugii
Armadillidium maculatum
Armadillidium nasatum
Armadillidium vulgare
Atlantoscia floridiana
Cylisticus convexus
Cubaris murina
Oniscus asellus
Porcellio dilatatus
Porcellio laevis
Porcellio scaber
Porcellio spinicornis
Porcellionides floria
Porcellionides pruinosus
Porcellionides virgatus
Rhyscotus texensis
Trachelipus rathkii
Trichoniscus pusillus
Trichorina tomentosa
Venezillo parvus
Others may be issued permits, but they're likely to require inspected containment facilities (which I don't have).
On a similar note, all the non-native mantids currently in vogue are being traded illegally. I checked with the USDA permit person to confirm this.
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