The downstream O2 sensor on OBD1 ludes (the one right in front of the cat) has this connector, and judging by how low the pigtail is in the wiring harness you should check that first if your car is OBD1.
1996-01 Acura Integra GS-R Downstream O2 Oxygen Sensor for L4 1.8L. 2000-01 Acura Integra Type R Downstream O2 Oxygen Sensor for L4 1.8L. 1997-98 Acura Integra Type R Downstream O2 Oxygen Sensor for L4 1.8L.
The ebay store page I've just posted unfortunately doesn't mention what the connector is called, and doesn't say that this part would fit a 3g, although clearly it would. I can't think of any other things on the back side of the engine bay that thing might plug into other than an o2 sensor. Check that out first and get back to us about it.
You might not have a leak if it's not obviously dripping. Every time one changes the oil filter on one of these, it dribbles all over the CV axle as you remove it and makes a huge mess. Most people don't clean the CV axle afterwards with a rag, so it gets shiny and might drip and throw droplets all over the place as it's driven. So, the mess you're looking at might just be the normal mess you'd see after just changing the oil and filter. Check things out in detail to make sure, of course, but if it's not actively leaking on you, it might not be something you need to worry about.
Cool! Well, we got one thing figured out. As for the oil leak, it's probably the sandwich plate gasket....or the O-ring in the filter itself is leaking, which I've also had happen because some debris (like a grain of sand or something) contaminated the seal. The sandwich plate gasket is probably pretty cheap, but you should try to watch the leak in action to determine that it is in fact the problem - put it up in the air, start it up, and let it run while you go underneath and watch. Take an inspection penlight with you if you have one so you can get up in there and see what's happening.