If you are eating less than 20 g/day of carbohydrate and are still breathing in and out, that is a good indication that you are producing ketone bodies. The urine strips measure excreted (unused) ketones, and some people’s kidneys are really good at filtering the ketones out of the urine and putting them back in the bloodstream. Even the blood ketone monitors are only measuring the ketones circulating in our bloodstream; they can’t tell us how much we are producing or how much we are using.
There is a difference between losing weight on the scale and losing actual fat. If your body is for some reason adding lean mass, that will make the scale weight appear not to change, even if you are losing fat at the same time. The number on the scale should be used in conjunction with such other markers as how your clothing fits. Since lean tissue is denser than fat, it is even possible for the scale to go up while clothing gets looser and looser.
If you are not losing fat anymore, there are a number of possible explanations: (1) you might not have any more excess to lose; (2) you might be consuming too much carbohydrate (some people have to limit themselves to even less than 20 g/day); or (3) you might be eating too little for your body to feel safe about parting with its energy reserve. So the first thing to try is to cut your carb intake even further. The next thing would be to add more fat to your diet. (And contrary to the standard advice, saturated and monounsaturated fats are much healthier than polyunsaturated.) Try to eat to satisfy your hunger, and don’t eat until you get hungry again. You might be surprised by the results.