On the night of May 31 or morning of June 1, half a tank of petrol was taken from a recovery truck that was parked at a premises in Smithfield Road, in Market Drayton.
The same night tracker batteries valued at about £1,000 were taken from a farm lane at Golden Hall, Hinstock, and a car was raided on the driveway of a farm in Cheswardine's High Street.
A handbag including its purse was taken from the car, and some of the contents were found dumped in a nearby hedge.
Between Saturday, May 1 and Monday, June 3, a bank card went missing after being used at a supermarket in Cheshire Street, Market Drayton.
Police said it appeared the card had been used to fraudulently withdraw cash from the holder's account.
Then on the afternoon of June 3, a shed at the back of a licensed premises in the Square, Woore, was raided and items taken.