Anorny is right. Let me illustrate by walking through your program in two passes. The first stage is the compilation stage. I've elided code that has no effect during compilation.

#!/usr/bin/perl -T

# implicit BEGIN blocks cause require and importing
use strict;
use warnings;

# here we define the object
{
    # creates a namespace
    package Animal::Hog;

    # creates, but does not initialize, a lexical
    my  $sound1;

    # creates, but does not initialize, a strict-friendly global
    our $sound2;

    # creates the function
    sub new {
        my $class = shift;
        bless {}, $class;
    }

    # creates the function, closing over the lexical $sound1
    # ... and binding to the symbol $Animal::Hog::sound2
    sub sound {
        my $self = shift;

        print $sound1, "\n";
        print $sound2, "\n";
        return 'knor';
    }
}
[download]

That's the compilation stage. Runtime looks like this, with irrelevant code elided:

#!/usr/bin/perl -wT

# call object method
Animal::Hog->sound();

{
    # assigns to the variable
    my  $sound1 = "knor1";

    # assigns to the variable
    our $sound2 = "knor2";
}
[download]

Execution happens in statement order.

(I also cleaned up your code slightly. Prototypes are useless on methods. Single-argument bless is almost always an error. The copy constructor technique using ref is also almost always an error.)