Three ohms sounds OK for the wiring, the fractionally higher than theoretical resistance is likely just contact resistance.
As long as it stays in low single digits when the cable is moved around, I'd not be concerned.
If it's a purpose made encoder cable the power cores are usually quite a bit heavier than the signal cores, sometimes massively so - so you may not get consistent readings across different connector pins.
Some are also double screened, with the overall outer screen to the machine metalwork & connector bodies, and an inner screen on the signal wires connecting through only to a pin on the CNC connector.
See the photo for an example - an offcut of Heidenhain cable for the 9 pin analog type encoders; the OD of the power cores is around the same as the jacket OD of each of the screened twisted signal pairs.
Any dirt inside the encoder is a worry - they are supposed to be completely sealed & that points to a problem elsewhere, such as the cable, gland or connectors being messed up.
I've seen them before now where the casing is flooded with oil because a connector is resting in oil and its seals are poor, allowing oil to saturate the cable and reach the inside of the encoder through the cable. Once they get to that stage, they really need replacing - or at least a new cable and very thorough soak in a bath of solvent..
If it's only a trace of dust or oil then wiping the disc with a lint-free cloth and trace of alcohol should do it.
RS sell packs of small lint free cotton patches that are good for wet-cleaning the optics in those and linear scales.
**broken link removed**
What make and model is the encoder - a Heidenhain ROD series? I have a few good used 2000 line RS422 output ones kicking about, but some CNCs need the analog sine output type or digital serial.
The dual rotary + linear feedback system makes it sound as if it could be a Siemens drive system / CNC?