Wow, lots of words with a wide variety of different meanings.
My mental picture of "somehow" is that there is this complex mechanism (how) that led to the outcome seemingly disconnected from the input and the speaker is trying to keep that a blackbox either because they don't know that mechanism or don't want to talk about it.
"Anyhow" to me is a means to cut the train of thoughts, or jump a little to somewhere that doesn't naturally follow. Or generally emphasize the disconnect between the input and the outcome.
Thinking more about it, my feeling is that these English words (and others, such as whatever and anyway) all generally introduce some gap in a train of thoughts, their difference is fuzzier, and different people use them differently. It's like shades of grey.
With that eyes, when I look at the long list, a few axis of classifications come to mind:
- Fog of 5W1H: Some words create a fog in "where" (e.g., 何処かしら), some in "who" (誰ともなし), "how" or causality (どうにか, なんとか), "when" (いつのまにか, 何かの拍子), and so on
- Level of formality: more formal words that tend to get used in the written form (e.g., ともあれかくもあれ, 何分, 何らか) vs less form words for speech (とにかく, どうか, なにせ)
- Rhyming attachments: Many of those words can accompany rhyming words to carry more emphasis. どうにか+こうにか, なんとか+かんとか, とあれ+かくあれ, なんでも+かんでも
Hope that helps!