This type of question seems to come up almost daily.
If you got as far providing the US embassy with your name and (probably more important) you're passport number, you might be challenged upon entering the USA, because your details might have been entered into the system as a visitor who requires a visa.
However, if you've not provided that information (and you're not on any international 'watch lists' as, say, a suspected terrorist), you'll almost certainly have no problem entering the USA (illegally) under the Visa Waiver Program. The US authorities have no direct access to the criminal records of any countries other than the USA and Canada (with whom they share a common database). As long as your convictions weren't in either of those countries, their immigration staff will be unaware of your convictions.
Over the past year, several people who've asked similar questions here have been kind enough to post again upon their return from the USA. (That included a guy with 2 convictions relating to class A drugs). They've all reported that they had no problems at immigration control.
Chris