with strong hand - or, “against the strong”; rather, “as a strong one” [Maurer]. Or, against the strong one, namely, Satan (Mat 12:29; Rev 20:2, Rev 20:3, Rev 20:10) [Vitringa].
arm - power (Psa 89:13; Psa 98:1).
for him - that is, He needs not to seek help for Himself from any external source, but by His own inherent power He gains rule for Himself (so Isa 40:14).
work - or, “recompense for his work”; rather, “recompense which He gives for work” (Isa 62:11; Rev 22:12).