Fetching system info using python
I would start by making your ip_list easier to understand. You could write a class for this, but using a collectins.namedtuple is a lot easier here:

from collections import namedtuple

Client = namedtuple("Client", "ip username passwd root_passwd")

clients = [Client("192.168.11.44", "root", "****", "****"),
           Client("192.168.11.8", "root", "****", "****"),
           Client("192.168.11.30", "root", "****", "****"),
           Client("192.168.11.6", "****", "****", "****")]


For the hard_disks, you could use the string module for all lowercase letters:

import string

HARD_DISKS = ['sd{}'.format(c) for c in string.ascii_lowercase[:19]]


For your repeated stuff, you could write a function:

def ssh_cmd(cmd, *args, root_passwd=None, **kwargs):
    stdin, stdout, stderr = ssh.exec_command(cmd, *args, **kwargs)
    if root_passwd is not None:
        stdin.write(root_passwd + "\n")
    return stdout.readlines()


This makes the rest slightly nicer to read. However, I would go further and put the other stuff in dedicated functions as well, which can then be put into a utils.py:

import string
from collections import namedtuple

Client = namedtuple("Client", "ip username passwd root_passwd")

HARD_DISKS = ['sd{}'.format(c) for c in string.ascii_lowercase[:19]]

def get_os(client):
    for line in ssh_cmd("cat /etc/*release", root_passwd=client.root_passwd):
       if any(x in line for x in os_check_list):
           # check for the obvious stuff first
           return line.split("=")[1]
    for os in ssh_cmd("cat /etc/system-release"):
       return os


def print_hard_disks(client, hard_disks=HARD_DISKS):
    for line in ssh_cmd("sudo -k udisksctl status", get_pty=True, root_passwd=client.root_passwd):
        if any(hd in line for hd in hard_disks):
            print(line)
        elif "command not found" in line:
            print("udisksctl not installed on target server")


def print_dmi_version(client):
    for line in ssh_cmd("sudo dmidecode -t 0 | grep -i version", get_pty=True, root_passwd=client.root_passwd):
        if "Version" in line:
            print(line)
        elif "command not found" in line:
            print("dmidecode not installed on target server")


It can then be imported in your main script:

import paramiko

from utils import Client, get_os, print_hard_disks, print_dmi_version

BANNER = """

******************************************************************

   IP ADDR = {}                SYSTEM INFO                           

******************************************************************"""

CLIENTS = [Client("192.168.11.44", "root", "****", "****"),
           Client("192.168.11.8", "root", "****", "****"),
           Client("192.168.11.30", "root", "****", "****"),
           Client("192.168.11.6", "****", "****", "****")]


def main(clients):
    ssh = paramiko.SSHClient()
    ssh.set_missing_host_key_policy(paramiko.AutoAddPolicy())

    for client in clients:
        ssh.connect(client.ip, username=client.username, password=client.passwd)

        print(BANNER.format(client.ip))
        print(" Operating System is {}" .format(get_os(client)))
        print_hard_disks(client)
        print_dmi_version(client)


if __name__ == "__main__":
    main(CLIENTS)