Just want to second what the previous poster said, too tight covers or diapers could actually be working against you. Same with too tight clothing, make sure there's no snug clothing around the diaper (like a diaper shirt for example) because if it's too tight it might be working it's way past the elastic on the covers and wicking moisture to clothing/bedding.
For the liners if you find you really need the 2 liners maybe try playing with how you're placing them inside. You might be able to find a way to minimize putting the bulk all in one spot, which would sort of 'lift' the cover and create a small gap. You could also try putting one or both liners outside the diaper. This won't help with bulk creating a gap at the leg in the cover, but it may help minimize any gap at the leg in the diaper.
Also make sure that your son's 'equipment' is pointed down and not upwards or sideways, that can make a big difference... Also maybe try playing with the liners to sort of form a bit of a pocket around his penis, to try to contain everything exactly where the most absorbancy is.
Are you using fleece or stay-dry liners? Is it possible they could have a build-up that's causing them to repel liquid? Maybe try going without for a little bit to see if it helps the leaks. If it does then either go without permanently or strip the liners to make sure they're build-up free.
It's always possible that he could be peeing large amounts very quickly and just overwhelming the diaper before it has a chance to absorb it all. It would be unusual for a baby so young but I suppose it's not impossible. The tricks above could help with that hopefully...
Side sleeper or not, the diaper should be able to absorb the urine and spread it around to the rest of the diaper. Really, regardless of how your little one is sleeping, the urine is 'coming out' in the middle of the diaper (more/less) where it should be being absorbed by the diaper/liners. Gravity may be pulling it a little to the side but it should still be staying contained in the diaper unless you've got something else working against you...
If you get really desperate you could always try using a cloth diaper & cover over top of a disposable. I'm positive you could make the cloth thing work but if not then this may be a workable solution to prevent those wet mornings all moms dread. The disposable would provide super duper absorbancy and probably absorb most of the urine, while the cloth & cover would 'catch' anything that leaks out and prevent it from going on clothing. I did this for a while when I really needed to use disposables but couldn't trust them not to leak. It's obviously not the most eco-friendly solution but then going through one or more sets of sheets and pjs per night isn't exactly all that eco-friendly either... Not to mention the unpleasantness of it!