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It depends whether you mean actual serious strawbale construction, like houses are built of sometimes... or just strawbales stacked to form a cooplike structure or the insulation thereof.
"Real" strawbale construction, a la houses, involves doing a proper foundation, then stacking strawbales on top, pinning them together with rebar +/or wire, covering with chcikenwire and then stuccoing. The strawbales can be structural, esp. for smaller structures; or they can be infill for a selfsupporting timber frame. It is not a major cost savings over normal house construction, and would be more work (though possibly same or less cost, esp if you produce good wheat straw bales on your farm) than a normal coop. OTOH it gives EXCELLENT insulation value, and has many other things to recommend it.
Anything short of that, where you're just stacking bales and hoping they stay put and weatherproof and predatorproof, is going to give you much less benefit. Stacking strawbales outside of a 'normal' coop can give good insulation value, although also has certain risks vis a vis rodents and rot. I would advise extreme caution, at *best*, if planning for stacked bales to be the actual structure of a coop -- they are heavy and if it falls over on you or the chickens, with or without the roof on, someone will get sincerely hurt. Or worse. If you have a pole shed type frame, strawbales could be used as infill, except they probably won't fit precisely to fill the walls and the same cautions about falling over still apply somewhat. I would not count on strawbales to be terribly predatorproof either, although they are certainly better than nothing.
For economy, your best bet would really be to put serious work into scrounging stuff -- you can get plywood, pallets, 2x lumber, old packing crates, sometimes even used sheds, for cheap or for free if you ferret around consistently enough.
Good luck, have fun,
Pat