A slash denotes the numeral zero, or the numeral seven. This is typically used in the military, or in European writing.
The "o-slashy", or Ø/ø, is a letter used in the Danish, Faroese, and Norwegian alphabets. It is not a variation of the letter o, but a different letter altogether. It is alphabetized at the end of the alphabet: ...z, æ, ø, å.