"photo" strictly refers to something captured by a camera. it's more formal than "picture" and is used more often to describe a picture from a news article or textbook. "photo" usually implies that the picture is professional and/or planned (as opposed to a spontaneous snapshot-- that would be a picture)
"picture" can also refer to a picture from a camera, but it can be used for other things like drawings. "picture" is the most common, and is usually interchangeable with the other two.
"image" can refer to something taken by a camera, but it also refers to slightly more abstract things. (for example, you are looking up at the sky and see the image of a heart in a cloud) if you are using "image" for a picture from a camera, it sounds more formal. you would most likely see it to describe a picture in a text book or news article.
I'm not sure how it is in other countries though. I can only speak for American English.