meaning in context

"In my hands" means that I am presently holding it. If I pick up a box, it is now in my hands. Normally you only use one hand to hold a phone so you'd say "in my hand", singular.

"On my hands" is normally used only for a few specific idioms. If you are bored or have nothing in particular to do, you may say, "I have a lot of time on my hands." If you are responsible for someone's death, you may say, "I have his blood on my hands". If you are stuck with something you don't want, you may say, "I'd love to come to your party but I have this screaming kid on my hands." Note this last is only used for undesirable things. You wouldn't say, "I have a winning lottery ticket on my hands".

It can also be used literally to say that you are wearing a pear of gloves or some other article of clothing worn on the hands. "I have my new purple gloves on my hands." Also if there is something stuck to your skin, like, "While fixing up the bedroom I got paint on my hands", or, "When I was in the garden yesterday I got poison ivy on my hands."

The only context I can think of where you'd say that you have a phone on your hands is the one I mentioned above about being stuck with something undesirable. Like, "The boss insists he be able to reach me any time of the day or night so I've got this annoying cell phone on my hands."

I don't think a fluent speaker would be likely to say "at my hands".

But "on hand" and "at hand" both mean in your possession or readily available. Like, "Our resturant has 150 pounds of beef on hand", meaning we have it in the storage room or someplace else where we can get it quickly. You might say, "I have a telephone at hand" or "on hand" to mean it is on your desk where you can pick it up whenever you need it, or otherwise nearby.