First things first. How did you install kernel 3.19? As you're running a LTS release, the recommended way to install new kernels is by Hardware Enablement. Kernel 3.19 is available in Ubuntu 14.04 repositories. Make sure you have it installed:
sudo apt-get install linux-generic-lts-vivid
Now, reboot the computer to load the new kernel. Make sure it is running:
uname -r
The above command should return something like 3.19.0-20-generic
. Now you can remove older kernels. Start with:
sudo apt-get purge linux-generic linux-image-generic linux-headers-generic linux-generic-lts-utopic linux-headers-generic-lts-utopic linux-image-generic-lts-utopic linux-signed-generic linux-signed-generic-lts-utopic
The above should remove the kernel meta packages which install updates for kernels 3.13 and 3.16. At this point, newer releases for kernels 3.13 and 3.16 will not be offered anymore, but the (possible) already installed kernels may receive updates. List the installed kernel packages:
dpkg -l | grep -E "linux-(generic|headers|image|signed)" | colrm 80
If you see any package with version lower than 3.19, remove it:
sudo apt-get purge <package name 1> <package name 2> ...
uname -r
.