Alan, I'll try to work you through the process. I'll reference the parts by the Moss drawing number in their catalog which you can get here http://www.mossmotors.com/Shop/ViewProducts.aspx?PlateIndexID=29295
First you will have to remove the brake drum. It should be held on by 4 bolts (item 33A) and a small phillips head screw (not numbered in the drawing, but shown just below the disc wheel type axle) With the drum off and the bolts and screw removed the axle flange (item 34) and bearing cup (item 32)will seperate and the axle should slide out. This is where you may have to use a slide hammer, but usually they aren't too tight. You'll probably tear the gasket (item 35) but these are available. When you get the axles removed you will know right away if you've broken one or both. When the axles are clear of the center section, then you can unbolt the 8 nuts that hold it in place and remove it for inspection.
What I suspect is that the small pin which retains the spider gear cross shaft (item 24) has broken and that shaft has slid out of the carrier (not numbered but shown just above the yellow number 21) and jammed against the housing and the spider gears (items 22) have dropped out and allowed the axles to turn freely.
Hope this helps, hard to describe all the bits and pieces.
'73 Midget (V6)
'59 MGA (I6) under construction
"There is a fine line between a hobby and mental illness"