Power of 2 is still a thing, yes. It's less to do with visual quality and more to do with efficiently using available device memory based on the way GPUs process data. Images don't have to be square, so your 150x50 example would fit into 256x128 instead of 256x256. This will get done by the GPU itself, so you don't have to manually resize the image to 256x128, just be aware that a 150x50 image will have the same memory requirements as an image that's 256x128.
Unless you're doing a hugely complex game with hundreds of unique animations, though, it's not something worth concerning yourself with. Mobile devices are pretty speedy these days.