Lots of OpenGL command takes enums. For example glEnable() can take GL_BLEND, GL_LINE_SMOOTH, GL_POLYGON_SMOOT, and many more.
But how does OpenGL process all this enum values?
A massive switch statement that checks for every possible values? or maybe more organized data structure like a map ?

Yeah a switch is one way to do it, another is to manually construct your own jump table (which the compiler may do for you with a switch), e.g.
void a( int arg ) {}//called if enumValue == 0
void b( int arg ) {}//called if enumValue == 1
void c( int arg ) {}//called if enumValue == 2
typedef void(Fn)(int);
Fn* table[3] = { &a, &b, &c };
void CallByEnum( int enumValue, int arg )
{
assert( enumValue >= 0 && enumValue < 3 );
table[enumValue]( arg );
}

Inside the driver, the code paths tend to be convoluted and so there really are a lot of "if (X) { callASetupFunction(); }" type structures. And, yes, that does mean there's a lot of testing needed to exercise all the sections -- and a lot of bugfixing about edge cases; "When I select X Y and Z, W doesn't work..."

It depends on the driver; OpenGL itself is just a specification and has nothing to say about this.