Delete all branches that are more than X days/weeks old

How about using --since and --before?

For example, this will delete all branches that have not received any commits for a week:

for k in $(git branch | sed /\*/d); do 
  if [ -z "$(git log -1 --since="1 week ago" -s $k)" ]; then
    git branch -D $k
  fi
done

If you want to delete all branches that are more than a week old, use --before:

for k in $(git branch | sed /\*/d); do 
  if [ -z "$(git log -1 --before="1 week ago" -s $k)" ]; then
    git branch -D $k
  fi
done

Be warned though that this will also delete branches that where not merged into master or whatever the checked out branch is.