If any of your recipes may be cooked in a crockpot, then use that. Ideally, your appetizers are a combination of hot & cold so that you can present them all together. Preheat your (hot food) serving platters in a warm oven or in the microwave. Chill your (cold food) serving platters in the fridge for a couple of hours (or in the freezer for 20 minutes) ahead of time.
There are warming trays and chafing dishes. However, in a pinch, be creative. Fold several damp kitchen towels and microwave them on a plate until very hot & steamy - seal each one inside a large ziploc freezer bag (minimal air) and place under your prewarmed platters. These will not warm the dishes but they may keep them from cooling too quickly.
There are regular hotpads on the market which do essentially the same thing for longer. Some are made to keep bread warm in a basket. Some disposable ones are even made for treating sore or cramped muscles but could probably keep a prewarmed glass or ceramic platter from chilling too quickly by placing it directly beneath the dish, on a cloth potholder. If you have an electric heating pad, it could be wrapped in a pretty piece of linen and lace, then placed under a very large platter as well. Again, these will only help reduce the heat loss, IMHO. Also keeping food covered as much as possible will help but try to avoid allowing the steam to ruin dry foods. HTH!