Borrowed around 1650 from Latin omnifārius, which is clearly omni-, all + some stem, but there seems to be some confusion exactly which. In five dictionary entries, I find the -fārius traced to fāriam, place/side; ferre, to bear; *fās, utterance; and facere, to do. It's a puzzler. You could almost say it has an omnifarious etymology ... but not really -- it's merely multifarious.
When I opened the door, the omnifarious colors stunned me -- it as if Maddie had dipped a dozen peacocks into Lisa Frank's paint cans and thrown them across her room.