Acknowledging those that have gone before with this one... I'd venture that there's a lot of Scots/Norse dialect at the root of the Newfoundland dialect, because the 'scurr' in scurrifunge is pretty clearly derived from the Old Norse 'skire' or 'skir', which had the meaning 'to cleanse, clear or purify'(c.1300) or 'clear of, free from, something morally bad' (c.1200)
Funge is interesting. According to the OED 'fung' is a common Scots variation of 'funk', which had the meaning (particularly of a horse) 'to strike or kick' and prance about kicking up dust (OED circa 1709). So a vigorous cleansing (with an element of chaotic energy and some disregard for gentleness) might be called a 'funging skirr' or 'skirring fung', hence (possibly) 'skirr-a-fung or scurrinfunge. Funk (as in 'blue funk') meaning cowardly or fearful probably comes from the same behaviours of a horse, but with the view that it's an undesirable trait, rather than an indication of vigour and alarming energy.