Azolla filiculoides tends to perish indoors, like duckweed it can be found in ponds or streams. Lemna minor seems to do well in tanks indoors at temperate of tropical conditions, it can be a bit of a nuisance to get rid of if you decide you do not like it.
I have Wolffia arrhiza in my daphnia drum, it disappears over winter and returns in the summer, never tried in in my tanks, as I fear, like Lemna it will become a pain to get rid of.
I have not seen Limnobium laevigatum, so cannot comment.
What sort of filtration are you looking at having in your killie tank?