Like this - each SATID has its own column in sorted order.

#!/usr/bin/perl -l

# http://perlmonks.org/?node_id=1186568

use strict;
use warnings;

my @secondpass;
my %keys;

while(<DATA>)
  {
  push @secondpass, $_;
  $keys{$_}++ for /SATID (\d\d)/g;
  }

my @keyorder = sort keys %keys;

for (@secondpass)
  {
  my %items = reverse /(SATID (\d\d).{27})/g;
  print join ' ', map { $items{$_} // ' ' x 35 } @keyorder;
  }

__DATA__
SATID 02 VAL1 32 VAL2 275 SIGNAL 43 SATID 24 VAL1 10 VAL2 098 SIGNAL 1
+2 SATID 41 VAL1 87 VAL2 180 SIGNAL 15
SATID 24 VAL1 41 VAL2 103 SIGNAL 56 SATID 02 VAL1 41 VAL2 154 SIGNAL 3
+1 SATID 41 VAL1 93 VAL2 124 SIGNAL 21
SATID 41 VAL1 23 VAL2 132 SIGNAL 23 SATID 24 VAL1 32 VAL2 034 SIGNAL 3
+2 SATID 02 VAL1 23 VAL2 145 SIGNAL 31
SATID 41 VAL1 63 VAL2 305 SIGNAL 62 SATID 33 VAL1 31 VAL2 174 SIGNAL 4
+4 SATID 02 VAL1 45 VAL2 205 SIGNAL 34
[download]

YES! This is perfect! =) Thank you so much. Can you explain (briefly) how the code works? I'd like to understand a little bit better what "magic" it is doing..

Can you explain ...? I'd like to understand a little bit better ...

You can gain insight yourself into the operation of this (or any) program by inserting print/dump statements at strategic points to see how data is extracted and transformed and how structures are built up:

use Data::Dumper;
...
my %keys;

while(<DATA>)
   {
   push @secondpass, $_;
   $keys{$_}++ for /SATID (\d\d)/g;
   }
print Dumper \%keys;

my @keyorder = sort keys %keys;
print Dumper \@keyorder;

for (@secondpass)
  {
  my %items = reverse /(SATID (\d\d).{27})/g;
  print Dumper \%items;  <STDIN>;
  print join ' ', map { $items{$_} // ' ' x 35 } @keyorder;
  }
...
[download]

The  <STDIN>; after the print statement in
    print Dumper \%items;  <STDIN>;
in the for-loop just pauses output until you hit Enter so you are not overwhelmed by stuff. (NB: My personal favorite structured data dumper is Data::Dump, but Data::Dumper is core. :)

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Give a man a fish:  <%-{-{-{-<