The below fix is especially difficult because of so many different memorials and pieces of memorials being involved. We will try to tackle the how to of this difficult repair but be aware that it cannot be made perfect again because there are so many unknowns that it is not possible to address them all. Unknowns such as all the places each stone originally belonged. There are a lot of clues to the repair and we will tackle these and we can make an improvement that will be significant to the historical preservation and beauty of the cemetery. At first glance we see only a bunch of scattered broken rock and some very large slabs and what appears to be one complete box tomb largely complete.  Looking closely we actually see parts of six box tombs in various broken stages and possibly some unmarked field stones. Here we will explore ways to reassemble the broken box tombs. To begin with we must document in place each broken piece before proceeding to move the parts back to be supported and reset in their original places. Nothing will be disturbed until we have a map or drawing of where each part is now and where it will be relocated. Also remember you have stones here that weigh from 25 to 700 pounds and any movement of a stone in the above scenario without assessing its place in the precarious balance of stones may bring a 700 lb rock tumbling down on you. So know what you are doing before tackling a project such as this. We do not have space for describing all the ways and means of safely handling large stones over 50 lbs so you will need to develop that methodology. That will take an ability to handle them without banging them around and breaking them even more and the main thing not getting yourself hurt. I will tell you it involves the use of special hoist that are cheap enough to build or purchase. These are known as Tripods. Tripods for cemetery restoration use vary from wooden "A" frame type capable of lifting up to two tons to the three pole steel I-beams frame that will support up to about five tons. 
Upon first surveying the disarray above one should see the following categories of possible stones:
1. Parts of box tomb including the main inscribed carved top, the box tomb sides, the end slabs.
2. Field stones that  mark nearby graves that are misplaced and left on top of the box tombs or nearby ground.
3. Field stones that serve only as fillers of the box tomb cavity. 
4. Other carved grave stones including misplaced footstones that actually may belong in another row of graves somewhere. 
Your first task is to identify each box tomb part to the respective tomb that it belongs. That is because these are the easiest parts to match up and will clear from the debris field many of the scattered parts making the rest of the task easier. You may use a digital camera and photograph each stone in place without moving any of them or just use old fashioned drawing paper and pencils. Make a corresponding record of each photograph numbering the stones for tracking purposes. For labeling purposes we can use the criteria as detailed here:
BTLS-Box tomb Left side Slab
BTRS-Box tomb Right side Slab
BTTOP-Box tomb Top
BTFE-Box tomb Front End Slab
BTRE-Box tomb Rear End Slab 
Note on site whether the stone is a part of a box tomb or field stone and try to classify the stones according to the above 1 - 4 classes. Note also the approximate age the stone might have been in the place where you find it. For example stones that have been lying in place many years are embedded in the ground deeper than ones lying on top. Stones lying on the box tombs for many years leave light colored spots where the mosses and lichens don't grow. That explains the light white spots in the pictures here. Clean stones are probably ones that have been moved or turned upside down where the mosses and lichens don't grow, but they might have also been buried below the ground and were dug up and placed on the box tomb top. It takes a few years for the untouched mosses and lichens to grow on a stone. Mosses will also grow on stones more protected from the sun though lichens will grow more where there is sunlight and moisture. Mostly these thoughts apply to the southeast where I am familiar with the plant biology of the wetter climates. That growth will give them the blackish/brownish molted look. The stone itself will age and change color over time but that is usually not noticeable is called patination. This process takes a 1,000 years for notable changes related to age to occur. That is at least for the hard types of stone used in memorials. Limestone, sandstone and marble can change quickly when subjected to the UV rays of the sun.
Deeply embedded fieldstones that are in the grave rows should be left alone, because chances are great they are grave markers or grave boundary markers. Even if you think you know don't guess at where anything might have been positioned. From this  information one can begin to conclude and make a record of the approximate age in place for each stone. You have it numbered and know its exact location. You can now make a drawing of where each stone will belong in the new order. Don't expect to know all of them just do the ones that are sure bets like you would on a Jig Saw puzzle. 
Your task when the recording and logging phase is done will be to begin reassembly of the box tomb parts. You might consider setting the broken sides in concrete at the bottom but be certain the concrete is not visible but below ground. This will hold the sides assuming there is not a flat base for them to set on. All four sides should be leveled nicely for the top to rest on. It becomes very tricky if one side slab is broken into lets say 10 pieces. Then you can and should use the approved epoxy gluing process to support the pieces. A box tomb part standing up can be glued whereas a top that is broken will collapse if you try to glue that because of the compounded weight on the glued joints. Go to the section on repairing broken stones and develop that knowledge. To repair broken tops one will need to use a combination of unseen supports installed inside the box to make that stand up correctly. When there is multiple breaks in a stone think of putting the parts together as you would a jig saw puzzle and the task will become less challenging. 
The preliminary layout below begins to show you how and where some of the missing parts are to be relocated back to their respective spots. To make the below image I used a large 2272 x 1704 or 5 mega-pixel digital photo and viewed and labeled the parts and then resized the photo back down to a standard 640 x 480 size that can be published. You can use the same method to document some of the biggest parts into their respective places. To do all of this from the photos you will need to take shots from several angles to aid you in eliminating the normal distortion that occurs from a photo in sizing or judging stone parts. So the best approach is to use a combination of drawings and photos.  I cannot show you the finished product because I did not see it nor actually do this repair.

These box tombs reside in the Greenwood cemetery in Columbia Tennessee.
for further information on lifting heavy stones see this URL on savinggraves.net
http://www.savinggraves.net/index.php/care-and-cleaning-of-cemeteries/1052-lifting-stones-with-a-tripod-hoist