0101 and +1 are used interchangeably to dial US phone numbers from a mobile (more on the plus sign).
When dialing from Japan:
to place international calls from Japan a carrier access code is also needed UNLESS you subscribe to a dedicated international plan; the carrier code is dialed before 010
the most used carrier access codes are: KDDI 001, SoftBank Telecom 0061, NTT Communications 0033