My first thought was cavernous abodes, but that's been covered, and more difficult on a level savannah or grassland, and more prone to flooding than in a mountain.
I do think they'd like shelter, even elephants get attacked by predators and can be killed and eaten by them. Particularly young elephants, don't forget about your infants and kiddos.
So I'll go with our own traditional housing; wood, stone masonry, bricks, etc.
The building materials do not have to be proportional, we build 2 story houses with stand-up attics, about 26 feet tall, using 2x4s and 4x4s. They stand up to most winds without a problem. I don't think it is a stretch to say that 6x6 timbers making a 30' house with 25' ceilings could be a tank against extreme weather of all sorts.
In more primitive circumstances, that could be log cabins built with tree trunks, and one of the simplest tools of early ages was an adze to flatten the trunks on both sides for stacking. Likewise, you can peg them together, and like early tribes, fill the gaps with mud, which can be supplemented periodically if rains wash some of it away.
If you are concerned about finding trees of width, primitive tribes in the past have built shelters from bundles of sticks, or even tightly bound dry straw, again packed with mud to glue them together. There is also the ancient practice of fired mud bricks, I would not discount that, the kilns are just found stones stacked and mudded together.
I don't consider your height requirement troublesome in the least for any of these strategies, just proportional sizing will take care of that. For example your giants would use fired bricks that fit in their hands. At over 3 times our size, perhaps over 3 times the size of our bricks in each dimension. Ours are approx 3.5 x 3.5 x 7.5 inches, so round up to 12 x 12 x 24 inches for your giants. Then it takes about the same number of bricks to build their shelter as it does ours.