Laos to Cambodia in a Lao registered vehicle should be OK but anecdotal evidence suggests it depends on the mood of the officials. One day they'll allow it, the next they'll state you need a Lao driver (and can only drive down to Stung Treng not to Phnom Penh) or a Cambodian driver's license. If you have the latter you should be OK. However, what I just referred to is for cars, for motorcycles it might be easier or then again it might be almost impossible.
Laos to Thailand is easy as but it's only straightforward for cars not necessarily motorcycles. Apparently motorcycles can only cross at crossings that don't have a bridge or perhaps if you are riding a big bike. There are no small motorcycles permitted to cross, either Thai or Lao registered at any of the busy crossings. There are never any differences between foreigners or Thais/Laotians crossing between the two countries by car or motorcycle. Both Thailand and Laos are straightforward but small motorcycles are definitely a problem - big motorcycles driven by foreigners may be easier to bring across than if you are a citizen of either country. I have never seen even one Lao motorcycle in Thailand and the only Thai ones in Laos are big bikes or train bikes, never 100 or 125cc scooters or motorcycles.
Crossing to a third country (e.g. Lao registered vehicle in Cambodia directly to Thailand) may be possible if you are LEAVING Cambodia for Thailand but you definitely won't be able to bring a Lao car or motorcycle into Cambodia directly from Thailand. In general, you must only cross directly between Laos and the foreign country you are heading to. If you want to visit both Thailand and Cambodia on the same trip you should consider first going from Laos to Thailand, then back into Laos to get to Cambodia.
