although the Dictionary of American Regional English (DARE) doesn't go into great detail on origin, as its focus is on area of usage, it has a wealth of interesting stuff (complete with crossthreads) on this word:

sigodlin - adj, adv
Also sidegadling, sidegarlin' sidegodlin, siebegodlin, si-godlin
esp. Appalachians Cf. anti-godlin, si-antigodlin, si-gogglin, si-waddlin

askew, lopsided, uneven; cater-cornered, diagonal(ly)
slantindicular
"You sawed that off a little si-godlin."
something that has got out of proper shape: [aside: gone all pear-shaped?]
"That house is all sigodlin."

Appalachian Journal (1976): Four terms suggest something out of line or out of plumb:
catty-cornered, cattywampus, slaunchways, or sigodlin