house

[khay]

He built a house for himself in California.

Does this mean he did the construction work himself or could it be that he had a house built for him?

[Marylin]

He built a house for himself in California.

Does this mean he did the construction work himself or could it be that he had a house built for him?

It means he either built the house for himself by himself (this is not specified) from the ground up.

or

He built the house for himself using others ( family members perhaps, contractors, friends). Also from the ground up.

If you want to be very precise as to who built the house, you can say:
He built the house by himself (jack of all trades - he would be the carpenter, the electrician, the plumber all in one - it would be a lot of work!).