What is the typical resistance across the various terminals of a MC phono cartridge?

Assuming you are referring to a low output moving coil cartridge, depending on the particular cartridge the resistance between + and - for a given channel probably falls somewhere between one ohm and a few tens of ohms, depending on the particular cartridge. Some manufacturers include that information in the specs they provide, and some don’t.

The resistance between either terminal of one channel and either terminal of the other channel should be very high, essentially infinite.

HOWEVER, in the absence of good information to the contrary I would not recommend measuring any such resistances with a multimeter. My concern would be that the test voltage applied by the meter might harm the cartridge.

Regards,
-- Al

Pretty much EVERY MC cartridge provides this information in their specs.  I recall values ranging from 5 ohms to 40 ohms.  But I'm probably erring.

Applying DC across your cartridge is a big no-no and may well have damaged your cart (assuming you used a multimeter to try and measure the coil resistance)

Long discussion of this topic here in the context of some designs of demag circuits that may output DC
https://forum.audiogon.com/discussions/mc-cartridge-degaussing-demagnetizing

Having said this the current generated by a multimeter at the lowest resistance range measurement setting is probably <1mA, in other words in the same sort of range as that generated by the cart in use so you may be OK -- but don't make a habit of it

This thread piqued my curiosity sufficiently to prompt me to make a measurement, using the two multimeters I have. One is a very high quality Fluke 87V digital multimeter, which can measure extremely small amounts of current. The other is a Triplett 310 analog multimeter. I set the Triplett to the Rx1 scale and used the Fluke to measure the current the Triplett provided with the lead of each meter connected directly to the corresponding lead of the other meter.

The Fluke indicated a current of about 7 ma, with the Triplett indicating a load resistance of close to zero ohms.

When I tried going in the other direction (using the Triplett to measure the current provided by the Fluke with the Fluke set to measure resistance), the Triplett presented too much resistance to allow a meaningful measurement to be taken.

A low output moving coil cartridge putting out 0.5 millivolts, a typical number for many LOMCs under the standard test conditions, and loaded with say 100 ohms, would be supplying and conducting a current of 0.5 mv/100 ohms = 0.005 ma, vastly less than the amount of current the Triplett meter supplied when measuring a near zero resistance. And the fact that a meter applies DC while the cartridge generates and conducts AC during normal operation may add to the possibility of damage.

The bottom line would seem to be what Folkfreak said above and what I initially suspected, that using a multimeter to measure the resistance of an LOMC is a no-no.

Regards,
-- Al