The lodging details below relate mostly to a list provided to me at Ryōzenji (霊山寺 - 1). It was kindly put together by Zenkon no Kai. and contains many places you can stay for free or at very little cost. I would highly recommend tsuyado. You stay in very simple temple accommodation and in the mornings you can join the morning prayer service. There are also many zenkonyado, some of which are really great.
Camping / Sleeping Out
If you are planning to camp or sleep out there are many places where you can do this. These include -
michi no eki - one of the many designated road side rest areas
henro huts - although not all are suitable for sleeping out
official campsites
under bridges
public parks etc
Maybe the most important thing that you need to be mindful of is trespassing on private residential property or stopping anywhere where you might inadvertently cause inconvenience to local people. There have been isolated cases of people using the larger toilets at certain michi no eki which has led to some complaints. The people of Shikoku are extremely helpful towards pilgrims and walking pilgrims in particular. If you are unsure about whether it is OK to stop at a place or not, always try to ask or try to be as discrete as possible.