It's entirely possible to follow a standard strength training program with sandbags - the main issues you'll come up against are actually getting the bag into position for most of the lifts. For my heavy sandbag work I use a Brute Force Heavy Hitter (Heavy Hitter) and that loads up to 200lbs.
I'd really say that the key thing is to re-evaluate exactly what you want or need from your training. If it's to get a big deadlift and squat (and I mean BIG) then replicating that with a sandbag is tough.
But if you want to build useable strength and muscle then the sandbag is a great option. Trust me, if you can clean and press a 200lb sandbag then you're in the big leagues.
The other good thing about sandbags is that you can also add in lots of strongman-style work like load carries, platform loads, drags and throws. These are all great ways to build muscle and strength.
This is me with a 130lb Heavy Hitter: