It's odd given that OsmAnd is the most feature complete OSM app for Android that there are so few custom map styles for it. I know the weird format it uses is a contributing factor (I think everyone else uses Mapnik compatible styles). But I find all the included themes really hideous and haven't found a good alternative. There are really good raster styles for outdoor use, so if anyone has advice on adapting an existing theme for OsmAnd I'd be curious to hear about that.
OSM is basically a dataset. Everybody renders this dataset differently unless they are sharing a renderer. Android apps such as Maps.ME and OsmAnd do their own vector renders.
I think it might be possible via the Online Maps feature by adding an online source, but for that I'd need the url of the source. For example, I can pick CyclOSM as the map tile source both in OsmAnd and on openstreetmap.org.
...and add all the benefits of having online slippy maps, yes, nice way of telling the full story
I enable this when I want to zoom to a random place in the world without first downloading a 600MB map file, want satellite imagery, or indeed want to view different styles. I wish there was better integration, like being able to also search worldwide with online services when this view is enabled (but it's also not like I got time to implement that myself so I can understand nobody else has gotten around to yet, either).