Lets see a sketch of the circuits you've tried (and please use BLACK ink and a fibre tip pen so its readable even if you have to photo it with your phone camera. Hint: If you cant photo it in direct sunlight, use as much artificial lighting as possible, as close as possible without getting in the shot) and photos of the actual circuits and all parts involved. Give exact part numbers of all chips, transistors etc. involved, and if you know, whether they came from China, or another country.
I'm not surprised you get inconsistant results for your 0.15R shunt. Most multimeters don't really give good results below one Ohm. To measure resistance down there you need to pass a known current through the resitor and measure the volltage across it and do the math, or use a really good meter that does four terminal resistance measurement.
I'm assuming you don't have a reasonable well calibrated bench PSU with adjustable current limit. If I'm wrong, use it and ignore the bit about the LM317 and 12R resistor below.
Take a 12 ohm resistor (anything from 10R to 15R would do), and connect it and a working LM317 (that you know regulates OK) as a simple fixed current sink. Use a PSU you know can maintain a reasonably steady voltage while providing 0.1A.
Leave it running a while to thermally stabilise. Measure its Isink (or the PWU's constant current if not using a LM317) with both meters in series. Now add your unknown low-Ohm resistor in series in place of one of the meters, and measure the current on the remaining meter, and the voltage directly across the low-Ohm resistor's leads with the other meter. Then swap the meters and repeat. Then measure the voltage across the low-Ohm resistor with both meters. Finally repeat all the measurements so far in reverse order to allow for any drift in Isink due to the LM317 heating up.
Average the currents and the voltages (after throwing out any readings that are way out of line with the rest) and use Ohms law and you'll be about as close as you can get with uncalibrated low cost meters. If the readings don't make any sense, suspect a problem with one of the meters - you'll find out if any of their test leads are intermittent!
Once you have confidence in your meters, you'll only need one voltage and one current reading to measure future low-Ohm resistors.
Build an accurate x10 OPAMP buffer and a precise 100mA current source, and you can apply the current to a resistor, connect the x10 buffer across it and directly read its resistance in milliohms as milliVolts at the OPAMP output.