It depends on your circumstances, and on such things as the age of the child and notice (i.e. the utility would have to be notified properly, if you are claiming special circumstances.)
You may want to look at http://www.massresources.org and call your local state agency.
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Oil companies are not regulated monopolies like the gas and electric companies. They can refuse to do further business with you until the outstanding balance is paid. You can try to do business with another supplier.
Disclaimer: This site exists to provide information only. It is not legal advice. Answering your question does not create an attorney-client relationship. I am a Massachusetts lawyer. Any information provided on this site does not, except as explicitly stated, imply familiarity with laws or procedures peculiar to your state which may differ from those where I practice.