Storage of methane in mineral oil or other liquid hydrocarbons
"Practical" can mean different things to different people, so I am not going to comment on that. 

Instead I am going to address the question, of solubility of methane in hydrocarbons, without any thought about "practicality" :)



This graph is taken from the book: Fuel and Lubricants Handbook (a simple google search lead me to it, and the relevant section appears in the preview :))

The data is reported at $50\ \mathrm{^\circ C}$ and $ 5000 \ \mathrm{psig}$ (pounds per square inch gauge, ungodly non-SI units. ca. $3.4 \times 10^7\ \mathrm{Pa}$ according to an online conversion)

Also, the following table from this publication:



I did not read it in detail, but the data was collected in the vicinity of 1 atm and between $25$ and $200\ \mathrm{^\circ C}$

FYI: Of possible interest could be this paper.