How to represent multiple conditions in a shell if statement?

Classic technique (escape metacharacters):

if [ \( "$g" -eq 1 -a "$c" = "123" \) -o \( "$g" -eq 2 -a "$c" = "456" \) ]
then echo abc
else echo efg
fi

I've enclosed the references to $g in double quotes; that's good practice, in general. Strictly, the parentheses aren't needed because the precedence of -a and -o makes it correct even without them.

Note that the -a and -o operators are part of the POSIX specification for test, aka [, mainly for backwards compatibility (since they were a part of test in 7th Edition UNIX, for example), but they are explicitly marked as 'obsolescent' by POSIX. Bash (see conditional expressions) seems to preempt the classic and POSIX meanings for -a and -o with its own alternative operators that take arguments.

With some care, you can use the more modern [[ operator, but be aware that the versions in Bash and Korn Shell (for example) need not be identical.

for g in 1 2 3
do
    for c in 123 456 789
    do
        if [[ ( "$g" -eq 1 && "$c" = "123" ) || ( "$g" -eq 2 && "$c" = "456" ) ]]
        then echo "g = $g; c = $c; true"
        else echo "g = $g; c = $c; false"
        fi
    done
done

Example run, using Bash 3.2.57 on Mac OS X:

g = 1; c = 123; true
g = 1; c = 456; false
g = 1; c = 789; false
g = 2; c = 123; false
g = 2; c = 456; true
g = 2; c = 789; false
g = 3; c = 123; false
g = 3; c = 456; false
g = 3; c = 789; false

You don't need to quote the variables in [[ as you do with [ because it is not a separate command in the same way that [ is.

Isn't it a classic question?

I would have thought so. However, there is another alternative, namely:

if [ "$g" -eq 1 -a "$c" = "123" ] || [ "$g" -eq 2 -a "$c" = "456" ]
then echo abc
else echo efg
fi

Indeed, if you read the 'portable shell' guidelines for the autoconf tool or related packages, this notation — using '||' and '&&' — is what they recommend. I suppose you could even go so far as:

if [ "$g" -eq 1 ] && [ "$c" = "123" ]
then echo abc
elif [ "$g" -eq 2 ] && [ "$c" = "456" ]
then echo abc
else echo efg
fi

Where the actions are as trivial as echoing, this isn't bad. When the action block to be repeated is multiple lines, the repetition is too painful and one of the earlier versions is preferable — or you need to wrap the actions into a function that is invoked in the different then blocks.

In Bash:

if [[ ( $g == 1 && $c == 123 ) || ( $g == 2 && $c == 456 ) ]]

Using /bin/bash the following will work:

if [ "$option" = "Y" ] || [ "$option" = "y" ]; then
    echo "Entered $option"
fi

Be careful if you have spaces in your string variables and you check for existence. Be sure to quote them properly.

if [ ! "${somepath}" ] || [ ! "${otherstring}" ] || [ ! "${barstring}" ] ; then

$ g=3
$ c=133
$ ([ "$g$c" = "1123" ] || [ "$g$c" = "2456" ]) && echo "abc" || echo "efg"
efg
$ g=1
$ c=123
$ ([ "$g$c" = "1123" ] || [ "$g$c" = "2456" ]) && echo "abc" || echo "efg"
abc