Atriums or atria come from ancient Roman architecture. They were central to the house, occupied a couple stories and provided access to other rooms. See The Roman House and Wikipedia. These days, atria are common features of multi-story public structures, with huge windows and sky views. (Here is an example of the famous Schow Atrium at Williams College.)
According to the NOAD, the great room is
a large room in a modern house that combines features of a living room with those of a dining room or family room.
In this Wikipedia article, there is an excellent photograph of a two-story great room.
In your house, great room would be the ideal term for the space you describe. You say it is a versatile space, one that would combine living and dining. The term would even be more apt if that is the only living space on the lower floor. Foyer wouldn't work because your space primarily a living area. Also, living room, family room and drawing room are not adequate. However, front room is a completely acceptable term, as well.
The difference between an atrium and a great room in modern architecture would be thus: An atrium is a large open multistory space often found in public buildings functioning as the central access point to the rest of the building, a source of natural light and a multi-purpose space. A great room, however, is the main living area in a residential building, and it used for entertainment, relaxation, dining, etc.
It is possible that atrium may come full circle and regain its original usage in residential architecture. For now, however, the trend favors an industrial usage.
A loft is not always a simple structure. These days, converted lofts and loft apartments are all the rage, especially in cities where real estate is scarce. From what you describe, the three upper-level areas constitute a loft.
The area could also be a modified gallery of sorts, most especially because it has a "half-wall" that overlooks the living area. Galleries, however, are traditionally narrow. Here is the relevant definition from NOAD:
a balcony, especially a platform or upper floor, projecting from the back or sidewall inside a church or hall, providing space for an audience or musicians.
Attic should be ruled out, as it usually refers to an uninhabitable or unfinished space. Garret is a fancy, old term that has a negative connotation. These two terms are inappropriate for the simple reason that your upper level overlooks the lower one in a way. Thus, loft and gallery are the best choices.
The bottom-line is: you can name the spaces in your house any way you want. For me, atrium and gallery go well together, because it makes sense that a gallery overlooks an atrium. Great room and loft are more traditional ("proper/formal") names, and these also go well together.
Themes can also be used in naming rooms in a house. For instance, the designer or owner yacht-themed house might favor the terms galley, for the kitchen, and bridge for an upper-level that overlooks the lower level on both sides (but this is a digression).
If you fancied them, you could term these spaces the lounge and the garret, depending on the look and feel (either real or imagined) of your house!