Does the 2007 Honda Odyssey have daylight running lights?

Yes, Your 2007 Honda Odyssey, like almost all vehicles, has daytime running lights, and that's a good thing. In fact, some places, such as Canada, mandate the use of them. It's a safety feature to allow other drivers to spot Your car, and for You to spot theirs. If You want the DRLs to come on and they're not doing so, check to see if the fuse for them has blown. It's typically listed as just DRL or Daytime Running Lamp. You may also need to replace the bulb, if it's not coming on. The other thing to check is that You've not inadvertently shut them off. Or, perhaps, You want to shut them off despite it being a bad idea to do so. Some Odysseys just have a toggle switch on the headlight control knob, but others, You need to pull and hold the headlight lever towards You for around a minute; You'll see an indicator flash twice, at which point You know they're disabled. To re-enable, You need to pull and hold the headlight lever towards You again, but this time only for haLFA minute, until You see the indicator flash just once.