We model the production of OH+, H2O+, and H3O+ in interstellar clouds, using a steady state photodissociation region code that treats the freeze-out of gas species, grain surface chemistry, and desorption of ices from grains. The code includes PAHs, which have important effects on the chemistry. All three ions generally have two peaks in abundance as a function of depth into the cloud, one at A_V<~1 and one at A_V~3-8, the exact values depending on the ratio of incident ultraviolet flux to gas density. For relatively low values of the incident far ultraviolet flux on the cloud ({chi}<~ 1000; {chi}= 1= local interstellar value), the columns of OH+ and H2O+ scale roughly as the cosmic ray primary ionization rate {zeta}(crp) divided by the hydrogen nucleus density n. The H3O+ column is dominated by the second peak, and we show that if PAHs are present, N(H3O+) ~ 4x10^{13} cm^{-2} independent of {zeta}(crp) or n. If there are no PAHs or very small grains at the second peak, N(H3O+) can attain such columns only if low ionization potential metals are heavily depleted. We also model diffuse and translucent clouds in the interstellar medium, and show how observations of N(OH+)/N(H) and N(OH+)/N(H2O+) can be used to estimate {zeta}(crp)/n, {chi}/n and A_V in them. We compare our models to Herschel observations of these two ions, and estimate {zeta}(crp) ~ 4-6 x 10^-16 (n/100 cm^-3) s^-1 and chi/n = 0.03 cm^3 for diffuse foreground clouds towards W49N.
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