I occasionally take a darkly-oxidized copper penny and just lightly brush the surface of my strops with the edge of the penny, as if brushing some dust from it. Using a magnifier under bright light to inspect the penny's edge, it's easy to see if there's any abrasiveness left in the strop. Assuming there is, it'll immediately scrub the oxide from the edge of the penny and leave a bright spot. Works pretty well with green, AlOx/emery, SiC and diamond compounds. The more aggressive compounds like SiC & diamond will polish to a higher degree in that single pass. I've even noticed they'll quickly smooth & erase visible scratches, tool marks (from stamping) and other deep damage from the edge of the coin. And on a light-colored strop, it'll obviously leave a dark trail in the wake of the penny's edge.
The oxide from the copper penny is pretty soft, compared to hardened steel. So, if you do this 'test' and can't see much/any removal of the oxide from the copper, that's a STRONG indicator your strop could use some cleaning and/or refreshing. This is also useful if testing other 'mystery' compounds or improvised materials for stropping, to see if they have any chance to be effective at all.
Rubbing the spine of a nicely patina'd steel blade on a strop could also reveal if it's working. The iron oxide (black) is harder than the copper oxide, so it'll be easier to see how effective the strop is on the steel, if it polishes any of the patina off.
David