thats what i'd call a hose. In my head softlines are AN-style, Hoses are hoses, and hardlines are...ye...hardlines

You can use what ever std hose, just make sure it's oil resistant, correct size, and can deal with some really hot oil (~150C).
A hydraulic hose shop can usually provide you with nice quality hoses. Hydraulic systems generate alot of heat, so most of them are heat resistant.
Std hoses for cooling and fuel-systems does not meet the requirements to last vety long. most of them dont handle heat above 120C, and very few handles engine oil.
GL!