I thought Text::Balanced might be an appropriate module to use here but I haven't used it before. The following test indicates suitablility for your application; other monks (who might have used this module more than once) may have better ways of doing this.

#!/usr/bin/env perl

use 5.010;
use strict;
use warnings;

use Text::Balanced qw{extract_multiple gen_delimited_pat};

my $in_string = q{qwe  asd 'rty uio p' zxc "vbnm fghj" 123 4 ' @ & '};

my @tokens = extract_multiple($in_string => [ 
    q{ },
    gen_delimited_pat(q{'"})
]);

for my $token (@tokens) {
    next if $token eq q{ };
    $token =~ y{'"}{}d;
    say $token;
}
[download]

Output:

qwe
asd
rty uio p
zxc
vbnm fghj
123
4
 @ &
[download]