Obviously, it's nice when you can go prone or use a rest, except what if there is something taller in the way? I can't shoot very well standing up. I've noticed that I can shoot a lot better sitting cross legged, using one of my legs as an elbow rest for one of my arms.
Would you guys advise practicing from this position for hunting or simply practicing to improve my shooting from a standing position? Are many game animals shot this way and is it common to shoot better this way than standing up?
See if you can find any guys in your area that shoot or have shot any kind of 3-position competition. They might be able to give you some pointers. As far as being better Sitting than Offhand... who isn't? There's a reason people struggling w/ Standing in 3-position refer to it as 'Awful-hand'. Sitting is the next most stable postion to Prone for most people.
Otherwise... for sitting, there are a couple variants. The one I'm most comfortable with, as it was what I learned 'back on the ranch', is the 'Open Legged' version. Basically you sit straight down on your behind, w/ your legs out in front of you, drawn up so you can put your elbows on the insides of your knees. Works well, comfortable, and you don't have to work at it very much to be able to get into it in a hurry. There are cross-legged and crossed-ankle sitting positions; the cross-legged being basically sitting Indian style, w/ your elbows in the 'pockets' on the inside of your knees, and the crossed-ankle is similar by w/ your legs partially extended. Both are much more stable than the Open-legged, but much harder to get into consistently (especially if you are a little overweight... you will probably see a very pronounced pulse from the blood vessels in the stomach wall unless you loosen your belt and unbutton your top button of your britches first), and much more of a PITA as far as scope eye relief, and canting. The Open-legged is more similar to regular Offhand in that respect: rifle vertical, head in a fairly neutral position.
Offhand... about the only way to get better is to practice. Get a .22 and some of those swinging targets or something to plink at.
BTW, I'd suggest getting a sling, a good sling, not one of those flaky cobra jobs in the sporting good stores, but either a quick adjust or a leather military sling, and learn how to use it. Quickest way to steady up your position short of leaning against a tree or fence post. Presents some interesting issues as well... like don't let the stock directly contact the hard tree or rock, or the shots will go off in weird directions. Cushion it w/ your hand or a hat or something.
The shooting sticks are a very good option. I had a set of the collapsible Stoney Point 'Steddy-stix' or whatever they called them, fully covered w/ camo tape, strapped along the side of my Model 7 SS (similarly camo'd) in .260 Rem. Never should have got rid of that gun. Nice, lightweight, accurate, enough punch for pretty much anything I'm really going to be shooting at.
Another way you might concider steadying your shots is to employ a set of shooting sticks. The buffolo hunters of the past used them to good effect for long range, accurate animal shooting (maybe you could, too).
With a rifle sling and shooting sticks, you will find you will be very steady, indeed. Be sure to check your point of impact, as it may shift from no sling to sling or sling w/shooting sticks. The shift in bullet impact will not be very great, if at all, at short range but at "long range" you may notice a change.
Hope this helps.
By the way, I still have and use the shooting sticks I made for myself while at Quantico, VA, for the Marine Corps Scout/Sniper Instructor School (1979).
Former Special Operations Sniper. Rangers, Lead The Way!
All the advice given so far has been good. I too advise that you practice in as many position as time allows.
One thing you should consider, depending on how you hunt, is your hunting position. If you're stand hunting, like a lot of LR hunters do, it might behoove you to get a setup prepped well before season. Get a good seat and shooting rail, heck one of the ultimate tripods might be the trick, though I usually use just a good setup and a Harris Sitting bipod. You can't always predict where you're going to be when the critters walk out but why not have your hunting stand as ready as you can make it.