The quantity of which ingredients should be increased to raise the moistness of a cake?
Talking about the role of each single ingredient and how they interact is way too much for an answer here, and parts of it have been discussed in other questions anyway. So I will give a quick info on the recipe you linked: 

It has way too much flour. For a standard pound cake, you want equal weights of flour, sugar, fat and egg, and most muffins follow a similar ratio. Some of them add liquid. But what you have here is a recipe which adds 50 g of sugar, 55 g of egg and 60 g of oil to 130 g of flour. Luckily, the oats are soaked, so they are probably not sucking out additional moisture from the batter. But still, you should change the ratio to get a standard muffin. Or, better still, you can get a recipe that works instead of fiddling with a bad one; finding a new, good recipe is generally easier than repairing.