The headlights on 98 Civics are positive switched, not earth switched. How do I know? Well, I have electrical engineering qualifications, and have owned a 1998 Honda Civic since it was new. I also have a relay-switched headlight loom using 10 AWG wiring in mine, since I discovered when it was new it was dropping over 2 volts between the battery and headlights – it makes a big difference to brightness. By the way, if you don't believe me about the headlight switching, the service manual for USA/Canadian Civics is widely available free of charge as a pdf on the web, and they show the circuit diagram – battery (positive), fuse, switch, dipswitch, wiring, headlight bulb, earth! Toyota are the main car brand who routinely use earth switching for headlights, not Honda.
I also have the same problem with my plastic headlights, but managed to recently pick up a second-hand set cheaply on Ebay, with much clearer lenses, which I'll install soon to replace my set with cloudy lenses.
By the way, the headlights MUST be replaced with a set from a 96-98 model Civic – the 99/00 models had a slightly different shaped headlight, which requires the later model grille to fit. So you'll need both the later headlights, and the later grille, if you want to fit them. It's cheaper to just buy the 96-98 model headlights, and make sure they are the genuine Stanley articles – there are a lot of shonky Asian ones for sale on the internet, that will probably spray light all over the place. I'd try a wrecking yard to see if you can get some off a crashed car (as long as it hasn't been crashed in the front!) – if you can find one that's led a sheltered life mainly in a garage, the headlights won't have noticeable UV damage to the clear coat.