'Trainers' is more of a British way of saying it. In American English, 'sneakers' is sort of old-fashioned sounding. More commonly, we'd probably say 'tennis shoes' or just 'shoes.' In the past, people said 'cross-trainers,' also. Less seriously, you can just say 'comfy shoes,' like: ' I got my comfy shoes on.'
Кеды is probably from the Keds brand. I would probably just call them 'shoes.'