Green’s Dictionary of Slang

1. (orig. UK tramp) to cadge.

1891		Birmingham Dly Post 31 Mar. 3/4: The slang made use of by the genuine tramps is extensive and peculiar [...] Much of it is evidently derived from the gipsies [...] ‘Mong’ is the gipsies favourite term for ‘beg’.
1900–10		Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 102: ‘to do a mong’ is to beg, borrow, or cadge anything.
1914		Bulletin (Sydney) 1 Oct. 30/3: Like me, no doubt, his life was spent / In paying T.P. duns and rent, / And never left himself a cent, / But had to ‘mong’ on friends for cash.
1958		D. Reeve Smoke in the Lanes 32: Romanies have, for centuries, monged most of their clothing.
2006		D. Mitchell Black Swan Green 304: Books never taught a man to mong or ducker.

2. (Aus.) to pursue, to chase after.

1896

Coburg Leader (Vic.) 7 Mar. 4/3: Passion and Cigar butts are always monging after girls.