Hmm interesting. Is the straw compressed?
I wonder if you could encapsulate straw with fiber reinforced plastic. That would make it properly watertight for a tiny house. You could even vacuum seal it or replace the air with an insulating gas / CO2. And theoretically the straw could then work as something a bit like a core material. Something like 1mm fiberglass is only like 5€/m² so a combination of those two could make for one of the cheapest building material. Ideally you'd use basalt instead of fiberglass and a more eco friendly resin, but the encapsulated energy for a tiny house is so little it doesn't matter than much.