How difficult is it to find reasonable lodging (without advance reservations) at homes, farms, vineyards and budget hotels while traveling by auto through Spain in the month of May?
No trouble at all. Except maybe for farms and vinyards which I know nothing about. I see 'habitacion' signs on places in the country. I have no idea what happens on the land it might just be a house in the middle of nowhere with rooms to rent. Hostals are good-value budget hotel. Note the spelling, it's not a hostel. Rather, it's a small, non-chain hotel, usually family-run, somethimes with really good local grub.
We stayed at a number of hotels in April that were very car friendly (ie Parking). Don't know your budget but they were in the $100E per night range. Some hotels were in the city and some were out of town. We can recommend accomodations in Salamanca, San Sebastian, Valencia, Grenada, Tarifa and Sevilla. If this price is within your budget and you would like their names and phone numbers, please reply.