It seems the problems you are having with your apple trees are indicative of poor growing conditions. The sooty deposits is something called ‘Sooty Mould’ which is a secondary condition, this grows on the honeydew excreted by aphids living on the leaves above. Get rid of the aphids above (which usually live near the ends of the shoots)and the sooty mould would die out. It sounds like you have already pruned your apple trees and this will help.
Nonetheless, because the trees are not growing very strongly, it is more than likely that these problems are going to continue. Therefore, I would suggest that you need to start to improve the fertility of the soil around the apple trees and then they would be better able to resist any pest and disease attack. You may also like to consider having your soil tested by http://www.thefertileearthconsultancy.co.uk who would be able to advise you on the best ammendments that would be needed to improve the health of your trees.