The distinctions are somewhat fuzzy - there is no absolute answer.

Microcontrollers (MCU) tend to be aimed at embedded control applications; they tend to consist of a processor plus a number of useful peripherals (MMU, Timers, watchdog, A/D, etc, etc, etc).
eg 8051, 6811, PIC.

Microprocessors (MPU) tend to be aimed at computer applications; they tend to have minimal "extras" on-chip.
eg Pentium

CPU means "Central Processing Unit" - this could refer to the actual procesor part of a microcontroller, the microprocessor within a computer, or the processor "box" of a computer system (which may or may not be microprocessor-based).