I have a 2003 EX I had just swapped with a JDM engine because my old one had gotten “crank walk” from a very excessively big stage 3 clutch previous owner put in. I had it swapped with a JDM engine with less than 60k or so that is what the importer I bought it from in NYC said. I put new plugs, thermostat in it and when I got it back from
the mechanic I noticed 2 days later coming to a stop before work my oil light came on. Checked it after work and it was pretty much really low on oil like empty almost so I added a quart and drove home about 20 miles. Next morning after I woke up there was oil on my garage floor. And then noticed my oil light come on again after work, checked it and low again and it does smoke really bad.. what could this be from?

Since the exhaust literally runs right under the engine, almost every oil leak can result in smelling burning oil.

top to bottom,
Spark plug tube seals
Oil cap gasket
Valve cover bolt seals
dipstick o ring
cam shaft seal
cam shaft plug
Valve cover gasket
Rocker arm sealant
head gasket
oil Pressure switch
pcv Valve or plate
block
Oil filter
oil pump oring
rear oil seal
crank oil seal
oil pump sealant
rear sealant
oil pan gasket
oil pan
drain bolt

if I forgot someplace you can be leaking oil, please forgive me.

Anything else besides your drain plug and oil filter being loose and I would take it back to the JDM shop you got it from.