There are many backpackers throughout Fiji on the main island and some of the smaller islands. These are very cheap and dorm style accommodation can start at around $20 per night.
Some villages have dorm style accommodation in their meeting rooms or bures.
Indigenous Fijians live in villages and sometimes offer accommodation to tourists in their homes. Fijians are very hospitable. Running water is not available in some homes and toilets are mostly outdoor communal toilets. Their homes are often made of corrugated iron and are very basic. You could expect to pay $30 per night including your evening meal.
There are a few Air BnB properties around Fiji. A lot of them are in main towns and owned by Indo Fijians.
Fiji has accommodation for different budgets. If you holiday in low seasons you may be able to negotiate a good deal.
Only enter a Fijian village with permission. Ladies should wear a sulu (sarong) or have their legs covered. Make sure you remove hats and sunglasses whilst in the village. If offered kava it is polite to accept.