Simpler way to check if variable is not equal to multiple string values?

For your first code, you can use a short alteration of the answer given by @ShankarDamodaran using in_array():

if ( !in_array($some_variable, array('uk','in'), true ) ) {

or even shorter with [] notation available since php 5.4 as pointed out by @Forty in the comments

if ( !in_array($some_variable, ['uk','in'], true ) ) {

is the same as:

if ( $some_variable !== 'uk' && $some_variable !== 'in' ) {

... but shorter. Especially if you compare more than just 'uk' and 'in'. I do not use an additional variable (Shankar used $os) but instead define the array in the if statement. Some might find that dirty, i find it quick and neat :D

The problem with your second code is that it can easily be exchanged with just TRUE since:

if (true) {

equals

if ( $some_variable !== 'uk' || $some_variable !== 'in' ) {

You are asking if the value of a string is not A or Not B. If it is A, it is definitely not also B and if it is B it is definitely not A. And if it is C or literally anything else, it is also not A and not B. So that statement always (not taking into account schrödingers law here) returns true.

You can make use of in_array() in PHP.

$os = array("uk", "us"); // You can set multiple check conditions here
if (in_array("uk", $os)) //Founds a match !
{
    echo "Got you"; 
}