According to Jisho, the expressions 何かと, 何くれ and 何かにつけて all mean "in various ways". However, I tried to search the difference in usage between them, but I couldn't find anything insightful.
To tell the truth, they are not expressions that I have seen in texts, but rather I came across them by chance while I was looking for another thing, and individually, one by one, I don't know very well how to use them. If possible, could you please, in addition to explaining the difference, give examples to understand these expressions better?
Edit: I wrote mistakenly 何につけて instead of 何かにつけて. I meant the second one from the very beginning, whose meaning in theory is "in various ways".