P,
Not an unusual tale - nature doesn't design animals to have muiltple births and all to survive every time.
Four likely causes
1. the pig uterous has two horns, joined to the central way out like this |-|-|with the central leg being the way out, and the legs either side being the horns. The piglets have to travel up a horn, (eg say from the bottom left vertical stroke of the M, and when they reach the junction they can go two ways they could go - either out into the wide world or into the other horn. If they go the wrong way (into the other horn) they generally reverse out (whe you see ones born backwards that is generally what has happened). However the cord breaks long before this, and after the cord breaks they have 5 minutes to get out or they die of oxygen starvation. It is likely that some of your ones died of this.
2. Once born they need to find the nipple, - if they go the wroing way (eg round her back) then they wander off and just die of cold and lack of milk
3. Mucous around the mouth or in the lungs prevent them breathing properly, and they die of oxygen starvation
4. Mum steps or lies on them - more often with new mums, but you can get dense sows that do this every time.
on 1. there is no cure, you cannot intervene as you don't know what's happening inside, and only when they are born fully formed but dead do you know
on 2 and 3 being there for the birth will help tremendously.
on 4. For a new mum, being there for the first few hours can help, but it generally takes the piglets 24 hours to learn to get out of the way, and by that time if you have a careless/thick mum it is too late. Heat lamp may help, but generally by the time they have found this, they have alreday learn't to get out of the way.
Finally, on burial, no you cannot bury them in the garden, this is illegal. You should contact fallen stock and arrange for them to be taken away, or take them to your local hunt, who will incinerate for a donation, or take to local incinerator who will charge. If you are going to breed regularly you need be able to show that you are correctly disposing of deadstock, as the authorites are rightly suspicious of breeders who never have any dead piglets.