catalytic converter

I just bought a 98 Honda Accord, V6.
Whoever owed the vehicle before me cut off
the catalytic converter. The car was cheap, it
was loud, but thought it may have a miss,
had to get pipe welded where converter was
to actually hear it. After having pipe welded,
the miss got worse, I don't know how to
explain it. But at 3,000 RMP's it gasps bad
and gas fumes fill the car. It get terrible gas
mileage. Ive had people tell me different
problems/solutions. The one that makes the
most sense to me is, its basically flooding
itself, without the O2 sensor that was in the
catalytic converter. That's what the sound
along with loss of power is, and gas fumes
and gas mileage all are from, and I need to
put one(catalytic converter) back on. What
is your opinions? Does that sound correct? It
was so cheap, i don't wanna give up