No. Wii games cannot run on Xbox 360. The architectures are fundamentally incompatible.
| Component | Wii | Xbox 360 |
|---|---|---|
| CPU | PowerPC 750CL "Broadway" (729 MHz, single-core, in-order) | PowerPC "Xenon" (3.2 GHz, 3-core, 2-threads each, in-order) |
| GPU | ATI "Hollywood" (243 MHz, fixed-function TEV pipeline) | ATI "Xenos" (500 MHz, unified shaders, 10 MB eDRAM) |
| RAM | 88 MB (24 MB 1T-SRAM + 64 MB GDDR3) | 512 MB GDDR3 (unified) |
| Media | 12 cm Wii Optical Disc (4.7/8.5 GB), proprietary format | DVD-DL (8.5 GB), standard UDF |
| OS | Broadway IOS (microkernel, per-game) | Xbox 360 OS (NT-based, hypervisor) |
If you have Wii discs, a used Wii ($30–$50) + component cable or Wii U ($100–$150) is the easiest legitimate path. For enhanced graphics, Dolphin on a modest PC is superior.