What did Mr. Otis offer the ghost? Why did he offer it?
Mr. Otis offers Sir Simon's ghost some oil. Mr. Otis wants Sir Simon to oil his squeaky ghost chains, so the chains won't make so much noise at night.
Soon after the Otis family moves into Canterville Chase, Sir Simon begins his haunting antics. The ghost's goal is to frighten the Otis family into leaving the house. He has been successful at this kind of thing for hundreds of years. He has no reason to doubt his continued success.
On one particular night, the Otis family has all gone to bed. Sir Simon begins moving through the house quite noisily. He is dragging a set of chains and manacles with him. The noise wakes up Mr. Otis.
Some time after, Mr. Otis was awakened by a curious noise in the corridor, outside his room. It sounded like the clank of metal, and seemed to be coming nearer every moment.
Annoyed, Mr. Otis gets out of bed, grabs a bottle of oil, and greets Sir Simon by the bedroom door. Sir Simon looks terrifying. He's got red eyes and ragged clothing, but Mr. Otis isn't fazed at all. Mr. Otis politely hands Sir Simon the oil and kindly asks that the ghost use the oil. That way his chains won't make noises that wake people up.
"My dear sir," said Mr. Otis, "I really must insist on your oiling those chains, and have brought you for that purpose a small bottle of the Tammany Rising Sun Lubricator. It is said to be completely efficacious upon one application, and there are several testimonials to that effect on the wrapper from some of our most eminent native divines. I shall leave it here for you by the bedroom candles, and will be happy to supply you with more, should you require it."