can i take a large corporation to a small claims

mavis tire shop, changed my tires to my car,and oil to my engine. Drove the car home the car was smoking out of the hood,opened the hood and the oil was coming out of the oil cap which they did not put back. Lost 2quarts of oil gushing out of cap.The oil also got on the outside paint, called the store the manager was not in and would have to wait till Tuesday I picked the car up on Saturday.I called the manager on Tuesday and told me to get the bill for the oil and the cleaning, The cost of the job was $326.00 I returned back to the tire shop the manager told me he never authorized that transaction, plus I needed a new timing belt which they serviced. Just got of the phone with a regional manager and told me they never paid that amount of money to get the car washed, so he would not agree to the price. I could not afford the cost of this cleaning as well but I was led to believe they would honor the invoice,plus I have been a loyal customer with 3 other cars as well. Need advise