Is this headed in the right direction?
Meaning does this code produce the output that you want? (given your single test case)...Program specifications are hard to write and I think the best way forward here is just refinement by example.

#!/usr/bin/perl -w
use strict;

my $input = '"non$volatile display" and ((timer oR count$3 Or display)
+ near5 hour).ccls. NOT (LCD).ab.';

my @omissions = qw(terms and or not with near same xor adj);
my $omit = join("|",@omissions);

$input =~ s/\..*?\.//g;
$input =~ s/$omit//ig;
my @searchterms = ($input =~ m/".+?"|[a-zA-Z][\w\$]+/gi);
print "@searchterms";

#prints:
#"non$volatile display" timer count$3 display hour LCD
[download]

update:
-I think that you mean for these .xyz. terms to be deleted?
-Above doesn't allow for terms in @omissions to be taken absolutely literally. I need to look in Larry's book for the syntax. But this does show a dynamic regex. Also probably need to take into account that omit words should be on boundaries (whole words - not words within words, the \b - look in Larry's book)
-Running substitute operations can take some time as the string is modified after each one, but this may or may not matter time-wise.
-The question right now: is this is "right" output? I mean for this given single input case?

As a general approach, I try to break these complex things into multiple easier steps. Get the right output, then tweak it if performance is not adequate.