We should both look up the dictionary definitions, but I'm just going to give some answers off the top of my head. I'm a native U.S. English speaker. There is a lot of overlap in meaning.
"Tool" suggests a mechanical device that acts on, shapes, or moves something else. A hammer drives a nail. A lathe cuts a screw thread.
"Instrument" suggests something that makes measurements--cockpit instruments like the altimeter, weather instruments like a barometer, lab instruments like a balance.
"Equipment" to me suggests a COLLECTION of things. When I was scuba diving, my equipment included mask, fins, tanks, regulator, watch, and knife.
"Device" suggests anything engineered to perform a function. A hard drive is a device, but it is neither a tool nor an instrument.
"Appliance" to me is short for "home appliance." I have a hard time defining it except by example: stoves, refrigerators, washing machines, vacuum cleaners, and "things like that."
"Apparatus" to me is a collection of devices, typically scientific devices, related to performing a specific task. It's almost the same as "equipment" but it is more formal.