Which county in Oregon has the largest population?

That would be Multnomah County,

home to two large Oregon cities, Portland and Gresham.

In 2010:

Multnomah County had a population of 735,334.

Portland has a population of 583,776.

Gresham had a population of 105,594.

Leaving just 45,964 in the unincorporated areas of Multnomah County.