Ubuntu root can't give any permissions?

Information about my Ubuntu:

No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 16.04.5 LTS
Release:    16.04
Codename:   xenial

I have a problem. I can't give any permissions nor change them as a root (sudo su, sudo -i etc). What should I do? How do I find the cause of this? How to fix it?

sudo nano test.sh

Output: Error writing lock file ./.test.sh.swp: Permission denied

Giving an user account its own permissions:

sudo chown -R student121:student121 /home/opilane121/

Output: Tons of Operation not permitted texts

Answer to comments:

1) NFS4 is read-write only

2) Output of mount | grep home:

mount | grep home
10.16.122.2:/data/users/students on /home type nfs4  (rw,relatime,vers=4.0,rsize=1048576,wsize=1048576,namlen=255,hard,proto=tcp,po    rt=0,timeo=14,retrans=2,sec=sys,clientaddr=10.16.122.146,local_lock=none,addr= 10.16.122.2)

The NFS-server is probably running with root_squash:

Very often, it is not desirable that the root user on a client machine is also treated as root when accessing files on the NFS server. To this end, uid 0 is normally mapped to a different id: the so-called anonymous or nobody uid. This mode of operation (called 'root squashing') is the default, and can be turned off with no_root_squash.

It basically maps root to a different user with least privileges. This is the default setting on NFS.

Talk with you server administrator, or if you are the server administrator, add option no_root_squash to the /etc/exports on the server.