Never signed a contract but told to report to work

If you like the number on your paycheck, the number just to the right of the dollar sign, and the check clears, I wouldn't worry about it.

In a certain sense, an offer letter does create a written employment contract, but the way they are usually worded, all they contain is the job title, place of employment, start date and rate of pay.  There isn't enough in one of those letters, usually, to take the employee out of an "at will" status, so you probably aren't losing anything by not getting one.