L~R's solution has problems:

$data_array_ref = [
    mykey1 => {firstkey => 'firstvalue', secondkey => 'secondval' },
    mykey2 => {ninza => 'turtle', 'Hurricane' => 'Dennis'},
    mykey3 => [ ['one', 'two', 'three'] ],
    mykey4 => [ [4, 5, 'three'], [6, 7, 'four'], [8, 9, 'five'] ],
];

for ( @$data_array_ref ) {
    print "$_ =>";
    if ( ref $_ eq 'ARRAY' ) {
        print join ", ", @$_;
    }
    else {
        print join ", ", sort values %$_;
    }
    print "\n";
}

__END__
[download]

output
======
mykey1 =>
HASH(0x1abefc0) =>firstvalue, secondval
mykey2 =>
HASH(0x1abf0a4) =>Dennis, turtle
mykey3 =>
ARRAY(0x1ab5148) =>ARRAY(0x1ab50d0)
mykey4 =>
ARRAY(0x1ab52f8) =>ARRAY(0x1ab5190), ARRAY(0x1ab5208), ARRAY(0x1ab5280
+)
[download]

My solution:

$data_array_ref = [
    mykey1 => {firstkey => 'firstvalue', secondkey => 'secondval' },
    mykey2 => {ninza => 'turtle', 'Hurricane' => 'Dennis'},
    mykey3 => [ ['one', 'two', 'three'] ],
    mykey4 => [ [4, 5, 'three'], [6, 7, 'four'], [8, 9, 'five'] ],
];

my $i = 0;
while ($i < @$data_array_ref) {
    my $key = $data_array_ref->[$i++];
    my $val = $data_array_ref->[$i++];

    print "$key => ";

    if (ref($val) eq 'HASH') {
        print join ', ',
              values %$val;
    }
    else
    {
        print join ', ',
              map { @$_ }
              @$val
    }

    print "\n";
}

__END__
output
======
mykey1 => firstvalue, secondval
mykey2 => turtle, Dennis
mykey3 => one, two, three
mykey4 => 4, 5, three, 6, 7, four, 8, 9, five
[download]

It be somewhat easier if your topmost data structure was a hash, not an array.

map { @$_ } @$_ flattens a ref to an array of arrays of scalars, as opposed to @$_ which only flattens a ref to an array of scalars.