use strict;
use warnings;

use Data::Dumper;

{
    local $/;
    $_ = <DATA>;
}

my %sequences =
   map  { $_->[0], $_->[1] }
   sort { length $a->[1] <=> length $b->[1] }
   map  { [split m{\n}] }
   m    { > ( [^\n]+ \n [^\n]+ ) }gx;

print Dumper(\%sequences);

__END__
>protein1
ASFGTHTRHTHRHTHTRHTRHTR
>protein2
ERYRYTRYHTRHTGEFEWWFEEFFFFREFRGRE
>protein3
AWEERERGRGRGREGRGREGRRRRRRRRTTHTHTRHRHTRHTR
>protein2
AASEFEFEFE
>protein4
REYTRHTRGRVEVCREVR