Hello,

The most common animals that eat berries are birds, rabbits, squirrels and other above ground omnivores, and deer. Deer and rabbits will strip off leaves and eat tender stems. 

Moles are insectivores, they eat mostly insects and a limited amount of vegetation. I doubt that moles are eating your shrubs. 

The best way to prevent this is to fence them (protects the whole plant) and net the plants ( protects fruit from birds). Here are some references on how to do that. 

Deer- check fencing often to be sure it hasn’t been pushed open-

https://snyderfarm.rutgers.edu/learning-center/deer-fencing/

http://www.canr.msu.edu/resources/deer_barriersfencing_repellents_dog_restraint_systems_e2672

Birds-

https://pss.uvm.edu/ppp/articles/birddamage.html

https://ag.umass.edu/home-lawn-garden/fact-sheets/bird-protection-for-blueberries-other-fruit

Rabbits, etc.-

http://msue.anr.msu.edu/news/how_to_protect_your_yard_and_garden_from_deer_and_rabbits

https://ag.umass.edu/sites/ag.umass.edu/files/fact-sheets/pdf/exclude_repel_wildlife_garden.pdf

Some combination of fencing or strong caging built from hardware cloth, netting across the top, and sturdy fence poles should protect you shrubs.

Recovery of the shrubs—-

The shrubs should leaf back out, if the stems still have bark on them, though it is late in the season. Protect them from being stripped again this summer and fall. Keep then watered to encourage recovery. Next year, return to your usual care program, following this pruning schedule:

Gooseberries- These produce most of their fruit on spurs that are located on 2- and 3-year-old wood. Canes (stems arising from the base of the plant) that are 4 or more years old are no longer productive; remove them when you prune. After pruning, a healthy bush should have 9 to 12 main canes--3 to 4 each of 1-, 2-, and 3-year-old canes. Remove all canes older than 3 years and canes that are damaged or diseased. Prune to form an open center and remove canes that are low to the ground.

After planting, a yearly pruning schedule would look like this:

Year 1. At the end of the planting year, remove all but 6 to 8 of the most vigorous canes during the dormant period. Make your pruning cuts as close to the ground as possible.

Year 2. At the end of the second season, leave 4 or 5 new 1-year-old canes, and keep 3 or 4 of the 2-year-old canes.

Year 3. Keep 3 to 4 canes each from 1-, 2-, and 3- year old growth.

Year 4. At the end of the fourth and following years, remove the oldest canes and keep 3 to 4 new 1-year-old canes to replace the older canes you removed.

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