Bash if statement with multiple conditions throws an error

Use -a (for and) and -o (for or) operations.

tldp.org/LDP/Bash-Beginners-Guide/html/sect_07_01.html

Update

Actually you could still use && and || with the -eq operation. So your script would be like this:

my_error_flag=1
my_error_flag_o=1
if [ $my_error_flag -eq 1 ] ||  [ $my_error_flag_o -eq 2 ] || ([ $my_error_flag -eq 1 ] && [ $my_error_flag_o -eq 2 ]); then
      echo "$my_error_flag"
else
    echo "no flag"
fi

Although in your case you can discard the last two expressions and just stick with one or operation like this:

my_error_flag=1
my_error_flag_o=1
if [ $my_error_flag -eq 1 ] ||  [ $my_error_flag_o -eq 2 ]; then
      echo "$my_error_flag"
else
    echo "no flag"
fi

You can use either [[ or (( keyword. When you use [[ keyword, you have to use string operators such as -eq, -lt. I think, (( is most preferred for arithmetic, because you can directly use operators such as ==, < and >.

Using [[ operator

a=$1
b=$2
if [[ a -eq 1 || b -eq 2 ]] || [[ a -eq 3 && b -eq 4 ]]
then
     echo "Error"
else
     echo "No Error"
fi

Using (( operator

a=$1
b=$2
if (( a == 1 || b == 2 )) || (( a == 3 && b == 4 ))
then
     echo "Error"
else
     echo "No Error"
fi

Do not use -a or -o operators Since it is not Portable.

Please try following

if ([ $dateR -ge 234 ] && [ $dateR -lt 238 ]) || ([ $dateR -ge 834 ] && [ $dateR -lt 838 ]) || ([ $dateR -ge 1434 ] && [ $dateR -lt 1438 ]) || ([ $dateR -ge 2034 ] && [ $dateR -lt 2038 ]) ;
then
    echo "WORKING"
else
    echo "Out of range!"

You can get some inspiration by reading an entrypoint.sh script written by the contributors from MySQL that checks whether the specified variables were set.

As the script shows, you can pipe them with -a, e.g.:

if [ -z "$MYSQL_ROOT_PASSWORD" -a -z "$MYSQL_ALLOW_EMPTY_PASSWORD" -a -z "$MYSQL_RANDOM_ROOT_PASSWORD" ]; then
    ...
fi