Removing kernel, I can't really help.
Regarding disk space, I doubt removing kernels will solve your issue at least on long term.
Tell us a bit more about your storage topology.
- Is everything installed on one single disk, including /var ?
- if you disk(s) is already full, there is no option aside clean-up but if space is used because of applications and components, clean-up will never be efficient enough.
Thus I suggest you look first at log files.
What's the result of:
sudo find /var -name *.gz | wc -l
This will tell you how many log files are there, as a very high level first step