I'm baffled as to why anyone would recommend eval for this. What you're asking for (though not what you should use) is clearly just another application of symbolic references. Of course, you're not going to get that to work without removing a stricture.

use strict;

my $string0 = "Jessy";
my $string1 = "Bob";
my $string2 = "Nancy";

for my $num (0..3) {
  no strict 'refs'; # Thanks for the correction, tinita
  print "${qq(string$num)}\n";
}
[download]

Common Beginner Mistakes has a good explanation of why you almost never want to use symbolic refs.