For what follows, I am referring to islands below Puget, and above the two Sand Islands near Ilwaco.
The float houses were placed by locals, many of them gillnetting families, many years ago, when nobody was regulating piling placement, sewage disposal, etc. There used to be many more than what your see today, including some sizable structures on land. In those days, none of the islands were part of a refuge, either. A few were private (Tenasillahee, for example). All of the islands except for a couple small disconnected accretions (from dredge spoils) are USFWS Refuge lands and are off-limits to overnight occupation currently, although I think there is one parcel on Marsh that was grandfathered in; there is one structure there, maybe another. Tenasillahee was acquired by the Feds in the early 1970's, the dairy structures were removed, and the pasturage was leased to a cattle operation, mainly to keep the grasslands open for better habitat for Columbia white tailed deer. [One day 10 years ago I ran across a guy in his 80's or 90's at Aldrich Point, who lived on Tenasillahee in the 1920's, before they had any refrigeration, and they converted all of their dairy out put to cheese and butter, marketing it via the steamer which came calling. He had some interesting tales to tell.]
All of the underwater lands on the OR side below to the State of Oregon, and the State can issue leases (and collect fees for the lease, typically very long-term). Restrictions on placing new piling make it virtually impossible to add any float houses, so that the floathouses you see now represent the relict population from days gone past. They can be bought and sold; the lease goes with the property.
Each float house is required to display a state plate, indicating the float house is permitted. I believe most have straight shot waste disposal, but I could be wrong on that. Some of the floathouses inside the John Day River (just above Tongue Point) I know are required to have holding tanks and are not allowed to discharge.
I think the County had some involvement in these things years ago, but they are now out of the loop.