It's not just Norse per se, but a broader Germanic mythology. In Old English the form was something like Wodin, but in Norse it was Odin.
As for why it's not pronounced like it's spelled, I believe it's because spelling was more or less standardized with the advent of printing, but pronunciation continued to change. Common words are especially prone to changes in pronunciation. The second syllable in Wednesday is unstressed, so it's easy to delete the vowel and turn the n into a syllabic consonant. Once that happened, there was a large cluster of consonants all pronounced with the tip of the tongue against the back of the teeth or the bony ridge just behind them, and when consonants cluster like that, some of them tend to get deleted. Strictly speaking, it's not a whole syllable that got deleted, but the end of the first syllable and the middle of the second.