Green’s Dictionary of Slang

1. something notably large, ‘a whopper’; also as adj., very large.

1898		R. Graeme From England to the Backblocks 82: Who was it I heard that in cutting-out some cattle on one of the Methvin plains, did come down a soliker and broke his horse’s knees? [OED].
1908		Aus. Mag. 1 Nov. 1251: sollicker Very big [GAW4].
1939		Franklin & Cusack Pioneers on Parade 168: She gave me a sollicker of a dose out of a blue bottle.
1941		Baker Popular Dict. Aus. Sl.
1955		P. White Tree of Man 91: ‘You can jump down, can’t you? You’re quite big, you know.’ ‘Of course he can [...] he’s a sollicker.’.

2. a large penis.

1950		‘No. 35’ Argot in G. Simes DAUS (1993).
1990		Tupper & Wortley Aus. Prison Sl. Gloss. 🌐 Sollicker. Penis.