What is a good way to get Outlandish artifacts..

…strange catches, etc. I need them for the Zong of the Zee

The nuns for strange catches, or Port Cecil. Best bet is hunting Lifebergs by Wither. Good rewards and relatively easy to farm as long as you know how.

And/or zee beasts around port Cecil, which also yield the hunting Trophies needed for the other components of the Zong.
edited by Ewan C. on 7/8/2014

One of the riddles from that recurring storylet yields a strange catch (I think it’s the 10 echo one.) Another recurring storylet with a strange beast can yield either that or a live specimen, but the challenges are quite difficult.

Outlandish Artifacts can come from a repeatable storylet off the Magician’s storyline, at Venderblight. Lots and lots of monsters have them in their drop tables (there seems to be one giant mid-tier drop table that most mid-tier enemies use.)