The stochastic oscillator compares the close with the recent range; the CCI measures distance from an average; Williams %R, the ultimate oscillator and a dozen others do close variants. All produce a bounded reading with overbought and oversold levels, and all are traded the same way: fade the extremes, or trade the crosses.
The claim is the same as for RSI: extremes mark reversals.
We tested the main oscillators, across their standard and non-standard settings, on 17 years of data with real trading costs. None showed an edge. Their signals are highly correlated with one another, since they measure nearly the same thing, and their results were the same: consistent with chance before costs, losing after.
The reason is the one on the RSI page. Adding a second oscillator to a first does not add information; it adds a second reading of the same movement.
If you trade it anyway, pick one, since they agree, and test it in a defined market state.