For those that haven't done any aeros, and don't know the difference between a barrel roll and an aileron roll:
A barrel roll is like a "corkscrew" in a roller coaster. Yes, there is some initial vertical accelleration ("g") when you pitch up, possibly up to 2 or 3g, but during the manoeuvre the "g" is pretty constant at around 1g. In any case it'll be somewhere between 1/2g and 2g. So it is a manoeuvre that falls well within the range of what any aircraft is capable of, IF (and that's a big IF) it is executed properly. For a barrel roll to be executed properly, you have to pitch up and roll in perfect harmony, while the speed is decaying, in order to be "on top" in both axis (pitch and roll) simultaneously. And keep the harmony going while the aircraft is accellerating again in the second half of the manoeuvre. It is far harder than executing the perfect chandelle. And if you do it improperly, well, number of things that can happen. You can fall out on top and end up in an inverted spin. Drop out the bottom and exceed Vne, or have to pull too many "g"s to recover. So although it looks simple (especially if you see one of those videos of people pouring coffee while doing it) but it is fraught with danger. In fact, at our club the barrel roll is considered an advanced aerobatic manoeuvre and is not taught in the basic aerobatics course.
An aileron roll is a manoeuvre with, in principle, no vertical accelleration. You follow a horizontal flight path, roll the aircraft with the ailerons while using pitch and rudder opposite gravity to keep the flight path horizontal. So from the normal +1G you go to a sideways force (through full rudder) with 0G in the vertical (aircraft) axis at 90 deg, then to -1G at 180 deg, then again 0G and a sideways force at 270 deg. Two things important here: most aircraft cannot maintain their horizontal flightpath with the rudder while being on the side, so most rolls use a more or less ballistic flightpath instead of a straight horizontal one. How ballistic this needs to be depends on the roll rate but about 30 degrees up at the start of the manoeuvre is usually enough. And if you don't have an inverted fuel/oil system, you lose engine power halfway through. The good news is, however, that there is not a lot of vertical accelleration throughout the manoeuvre, so the speed stays more or less constant. But if you have loose items in the back, they will be all over the plane. In fact, without an inverted fuel system, the engine will stop, the speed will decay because of the drag, and all items in the back will float forward. Not funny.
A hesitation roll is an aileron roll where the aircraft is momentarily fixed in position, by stopping the roll, at 45 degree, 90 degree etc. angles (in case of an 8-point). So at 8 times during the roll, the aircraft seems to hesitate.
So, yes, any aircraft might be able to perform the perfect barrel roll without being overstressed, or even drinks being spilled all over the place. But it takes a very skilled pilot to do it properly. And an improperly executed barrel roll will leave you without options (or even without wings) in a very short time.
Don't do it people.
Get a proper aerobatics instructor and a proper plane. I can tell you from experience it's a lot of fun but the easiest-looking manoeuvres are usually the hardest to fly.
Oh, and 4g just means that the sweat runs off your face and back four times as fast.