Clogged egr passageways.
Bad distributor.
Low compression.
Timing off, camshaft or distributor or both.
Plug wires.
Distributor cap, bad distributor.
Bad-plugged cat.
Low compression.
Valves not adjusted in ages.
Partially plugged injector.
Bad fuel pressure regulator.
Manifold gasket leak.
Cracked exhaust manifold, plugged exhaust.
Crap fuel.
Blown head gasket.
Many more possibilites or combinations of separate problems that could cumulatively result in the driveability problem. Without absolutely accurate service history and knowing all service was performed competently, this is a mechanics nightmare. Look on the net for a truly knowledgeable Honda specialist who might be willing to take on a diagnosis and if you find one, don't expect him to drop everything to take on your problems, because if he-she is competent and a successful business person, then he-she will have a serious backlog of work in line ahead of you.
While you may not like my answer, there really is no starting point without much more information.
regards
mech
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