ONlwSG

gad m. [ɡ̊ad̪̥], gen. gaid [ɡ̊ɛd̥ʲ], 

Cf. Dwelly 1911; AFB^˄.

goid [ɡ̊əd̥ʲ], 

Cf. Dwelly 1911; Dieckhoff 1932: [gö(i)dˈj].

‘a withe, twisted twig; [and by extension] a switch; a number of fish on a string or withe; a bend on anything’ (Dwelly 1911) is derived by MacMillan (in Christiansen 1938, 4: gad math de adagan is de bhod[a]ich-ruadh [‘a good withe’s worth of haddock and cod’], and 17) from ON gaddr m. ‘spike etc.’. McDonald (2009, 355–56: gàd, gàt ‘iron bar, withe, switch’) confuses gad with SG gàd m. [ɡ̊aːd̪̥] ‘iron bar etc.’ and sees ON gaddr yielding Scots gad yielding SG gàd.

From a phonetic point of view, ON gadd acc. would indeed be expected to yield [ɡ̊ad̪̥] in Scottish Gaelic, but Christiansen (ibid. 17) opines that SG gad is hardly Norse, comparing Ir. gad ‘withe’. SG and Ir. gad go back to EG gat ‘withe, osier; halter or fastening of withes or osiers’, 

See Matasović 2009, 155, s.v. *gazdo-: OG gat is possibly related to OG gass ‘sprig’, but unrelated to OG gataiḋ ‘steals’.

which is ultimately related to, but not a loan from, ON gaddr (MacBain 1911; OED^˄, s.v. ¹gad; de Vries 1962).

SG gàd m. [ɡ̊aːd̪̥], gen. gàda -[ə], has the senses ‘iron bar, large thick piece of anything; stalk; inherent propensity, in a bad sense’ (Dwelly 1911). The sense ‘iron bar’ probably derives from Scots gaud [gɑ(ː)d] ‘a bar of iron; spar; goad (for driving cattle)’ (SND^˄, s.v. ²gaud) (cf. Eng. gad), which goes back to MEng. gad, gadde (OED^˄: from early Scandinavian [cf. ON gaddr]).

Cameron (in MacBain 1894a, 632: gad, gat [sic]) suggests a derivation from OEng. gáde [sic] (Eng. goad, MEng. gaade, OEng. gad, gaad (inherited from Germanic (OED^˄))) ‘a spike or pointed implement’. While Eng. goad and gad are attested in similar senses and are sometimes associated with each other, they are apparently unrelated (OED^˄).

The sense ‘large piece of anything’ is conceivably an extension of the sense ‘iron bar’, but is reminiscent of Scots gad (for gaud) in the sense ‘(of ice) a large mass’ (SND^˄, s.v. ¹gad). The sense ‘stalk’ seems likely to be either an extension of the sense ‘bar’ or the result of conflation with SG gad ‘withe’. Finally, the sense ‘inherent propensity’ may be the result of conflation with a loan from Scots gate [get], [gɛt] ‘road; manner; conduct, habit etc.’ (SND^˄), with Dwelly’s ‘in a bad sense’ arising from the context of his example tha droch g[h]àd ann ‘he has a [b]ad turn of mind’.