use strict;
use warnings;

my ($key, %hash, @order);

while (<DATA>) {
    $key = substr($_,1,length($_)-2);
    $hash{$key} = <DATA>.<DATA>.<DATA>;
    push @order, $key;
}

# To look up a specific record:
$key = 'Record 3';
print "$key =>\n$hash{$key}\n";

# To output the records in order:
print "$_ =>\n$hash{$_}\n" for @order;

__DATA__
>Record 1
AGTCTAGTCAT
CATCATAAGAT
CATCAATCACA
>Record 2
ATGAACAGCAG
ATGAAGAATGG
ATAG
>Record 3
AGTCTAGTCAT
CATCATAAGAT
CATCAATCACA
>Record 4
ATGAACAGCAG
ATGAAGAATGG
ATAG