After you cross the border from Vientiane to Nong Khai I'd recommend train to Bangkok. Once you're in Bangkok, see this story for overland options to Siem Reap.
Re going through Laos, as Rufus suggests, I'd say break the drip up to see perhaps Kong Lor Cave and Don Khon at least. For crossing the border into Cambodia, see this story, from where it is straightfroward to get onwards transport to Phnom Penh.
Other alternatives are to fly from Bkk to Udon Thani with Air asia and then take a mini bus into Laos. Udon is worth a day or two. Somtam's suggestion of the Kong Lor Caves is a good idea. They are only a 5 hour trip from Vientiane. You can take a bus to Phnom Penh or fly from Vientiane. (My choice wuld be the latter).