I'll bite but I really don't know how to answer this one. Way too many variables in this one, as your question is a little to general.
1. Will a .308 kill an elk and how far is it effective? You have the best answer already as it depends on your shooting ability. That said if your shooting ability is up there, then we can just go with a benchmark of sorts. Let’s say you need 1500 ft-lbs (generally well accepted) of energy to kill an elk with a rifle. That means your cartridge will reliably kill an elk at what ever range you don't go below 1500 ft-lbs. So with this benchmark you should be able to reliably take an elk at almost 300 yards with a 165 grain bullet and almost 400 yards with a 180 grain. So if you stick with that kind of thinking you should be all right.
2. What is the best bullet to work at all ranges? Bullets are kind of like double edged swords at times. There isn’t one perfect answer. With the .308 it makes your bullet selection a little easier. If you go with 180 grains pretty much any bullet will do, as the bullet is going to retain enough mass to penetrate to the vitals on most shots, exceptions being extreme angles or TX heart shots at longer ranges. Make sure you don’t use too tough of a bullet or at the longer ranges it may not perform (expand) well at all.
If you go lighter than 180 grains for elk you’ll probably want to use a premium bullet. You will want one that retains enough mass to penetrate to the vitals to anchor the animal, but not so tough that it doesn’t expand at all especially when the velocity starts to fade. The Nosler Partition is a good standard to go by, as it truly was the first premium bullet and the one that works well across the velocity range.
Remember when John Nosler developed the first premium hunting bullet it wasn’t because he wanted a bullet that would work at long range. He wanted a bullet that would hold together and retain enough mass to penetrate to the vitals when it struck at close range at higher velocities. He had a bad experience with standard bullets when shooting a moose at close range with a .300 H&H in AK.
3. Remember hunting isn’t about being able to make the long shot. Hunting is a combination of a lot of different things. More of a mastery of your surroundings, being able to make that long shot is a good skill to have. However, so is your stalking skills, because until you have been able to close the gap to where you can smell that big bull elk without him knowing you are even there, and watching him urinate all over himself while bugling and chasing cow. Boy that will get your heart rate up in a hurry!
