It might be not the best way to do it, but for the regexp part I'd go with something like

use strict;
use warnings;

my $line = 'OPENINFO="Oracle_XA:Oracle_XA+Acc=P/NASIT/nasit+SesTm=60+S
+qlNet=QANASIT+LogDir=/users/nas/disk1/data/traces+DB=QANASIT+Objects=
+true+Threads=true"';

my $DBUser = '$DBUser';
my $DBPass = '$DBPass';
my $DBSid  = '$DBSid';

my $openinfo_rx = qr/ \A OPENINFO=" # openinfo line start
                         ( [^"]+ )  # whatever inside the '"'s
                      " \z          # openinfo line end
                    /x;

if ($line =~ m/$openinfo_rx/) {
    my $openinfo_content = $1;
    my $quoted_openinfo_content = quotemeta( $1 );
    my (@openinfo_parts) = split( /$quoted_openinfo_content/, $line );

    $openinfo_content =~ s{ =P/      # =P/ starts user/pass part
                            ([^+]+)  # whatever except +
                            \+       # end mark for user/pass part
                          }
                          {=P/$DBUser/$DBPass+}x;

    $openinfo_content =~ s{ \+(SqlNet|DB)= #
                            ([^+]+)        # whatever except +
                            \+             # end mark
                          }
                          {+$1=$DBSid+}xg;

    $line = join( $openinfo_content, @openinfo_parts);
}
print $line;
[download]

That assumes however that the strings used to anchor the parts that will be replaced won't never be also part of the text to be replaced - in your example, you migt have for example '+SqlNet=XXX+' instead of 'nasit' as password.
A supposition that might be true or not, so maybe the code would need to be tightened a bit if there are no known restrictions on the input data.

Hope that helps.

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