Note that use strict boils down to

BEGIN { require 'strict.pm'; strict->import(); }
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So strict->import() actually applies to the lexical scope one step outside of from where import() was called (or something like that). So, the following actually works:

package AID;

require strict;
require warnings;

sub import
{
    strict->import();
    goto &warnings::import;
}

1;
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Then:

use AID;
BEGIN { print 0+""; }
print $x;
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Gives:

Argument "" isn't numeric in addition (+) at - line 2.
Global symbol "$x" requires explicit package name at - line 3.
Execution of - aborted due to compilation errors.
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And diagnostics.pm isn't lexically scoped (and I'm not sure why people even use it, to be quite frank), so you can just "use diagnostics" inside your common.pm file.