If they aren't individually selectable, they're not deletable separately in object mode. They're probably part of the same object, weighted to their own bones.
If they're weighted to their own bones, you have a few options. One is to pose the model and enter weight paint mode (ctrl-tab from object mode), then switch to vertex select mode ('v' key) and ctrl-RMB lasso a whole bunch of vertices from the object you want to delete, now that it's nicely out of the way. When you tab into edit mode, those vertices will still be selected, and you can ctrl-l select linked to probably get the whole object for easy deletion. If not, delete, tab back to weight paint, rinse and repeat until you've got it all.
Another deal is that probably all of the vertices of the individual objects are exclusively weighted to a single bone. Select one vert in edit or weight paint mode, 'n' to open your properties shelf, and look at the vertex weights section. Here it will tell you which vertex group this vert belongs to; clicking on the group will select that vertex group for your model. Now you can look on the properties view, under data vertex groups, and hit the "select" button, which will grab all the vertices assigned to this particular vertex group. Which is probably the entire object, and only the entire object. Delete, and you're good.