itsmoked - sorry I got confused about your location. You have an even milder climate than I do in NW Washington (1 mile from ocean).
Both itsmoked and warpspeed, you need to try a tool to zero in on your heat losses and do a what-if. This can show you where you should put your dollars. Now no heat seems a bit extreme, but you still need to think about where to put the money. Here is one free package
you can download (172 MB). Wirsbo has one I used but you have to beg a bit harder. There are far more complex models available the can actually analyze walls and sunlight and stuff but they are real complicated and for academics and people really into building engineering.
Generally the ceiling has the higher losses than walls but zero insulation seems bad. Infiltration can be a real big factor. Load analysis will not tell you what infiltration rates are.
What follows is my $0.02 (US) on an approach.
Upgrades to the structure return savings each year. They are more effective dollars. Increasing fuel costs just make them better.
Find someone who can do a blower door test for a reasonable amount. They may be scarce in your area but you might be able to cobble something together yourself. It is a test where they put a blower in the door (duh) and measure the flow at a given pressure. Block you chimney.
Double pane glass is not all that bad particularly if it still works. Vinyl is also a pretty effective window material.
There are ways to insulate the walls. Not nifty but doable. With your walls the inside would be the way in. You can patch plaster better than redwood. It would be ugly and messey but you could put a hole in each stud bay and bring in someone to spray something into the bays. The something would be foam (expensive but high R value) or cellulose. The foam would seal better and also provide a vapor barrier. An alternate would be to put some foam sheets and a vapor barrier on the walls and cover with drywall. You loose some floor space and the penetrations (doors and windows) and electrical outlets need to be handled, but if fixes a number of problems.
The fireplace should have an external air supply. Figure out how to get a duct from the outside to the fireplace. If you have a crawl space this should not be too bad. Be careful - you do not want to creat a situation where the fire can get into the outside air supply unless everything is rated for this. It has to have a damper to close off the outside air when not burning. Put a damper on top of the chimney. Normal controls (particularly old ones) do not seal the chimney. It needs to be on the exterior vent where you can actually get a seal. A sealed glass door helps this whole effort if you can get the air supply inside the doors. Maybe a heat exchanger you can put in the fireplace and circulate some heated air (maybe back to where the kids are huddled under the blankets). Dryer has the same issues. Get outside air with a damper to it and close the door to the laundry room if there is one. Do not vent the dryer to the inside. Bad water vapor problem and small lint in the air.
I am guessing that "foundation- raised" means a crawl space. Insulation and a vapor barrier are relatively inexpensive and you can do it yourself if you do not have a thing about spiders (I do). Air infiltration should be a part of this. You might consider fiberglass batts between the floor joists and then a vapor barrier. The fiberglass with an integral vapor barrier is hard to actually seal. Unfaced batts and poly seems better. You could also do sheet foam and seal the edges. Foam/tape any penetrations. You may need a plastic film on the ground to keep humidity down in the crawl space. Every place you have a pipe or wire going through a wall you will lose energy. The top plate of your walls probably leaks much air into the attic. Ceiling lights (especially recessed) leak a lot. Be careful sealing and insulating lights. They may not be rated for insulation contact. One way is to make a box out of something (there is a ceramic based board used to line commercial range exhasusts) to cover them and then seal that box to the ceiling. Push aside your attic insulation and seal wires, vents, and tops of walls with foam in a can. Be careful about your insulation. You should know what it is before you fool around up there if it has been there for amny years. Make sure there is nothing but fiberglass. Some old granular materials can contain asbestos.
Spray foam on the children. Nah, this makes them too inflexable.
Windows can be improved with another layer of glazing. Adding storm windows can help but an economic analysis will drive this approach. A piece of plastic (not a film but an actual sheet of plastic) can be added to the window. This can be internal or external and removable for the summner. You can use those strips of flexable magnet like on a refrigerator door. Those window air conditiners are probably big leakers. Make some insulated drapes for the windows that can be closed at night. If you or you wife are a bit handy and have a sewing machine that is not hard. Use some fiber insulating batt inside. Put the edged is some sort of track to reduce convevtion losses. Or do the macnetin strip thing.
Upgrade air seals on the doors and windows. Sliding glass doors are particularly bad performers.
The heating system. I have to assume there is some sort of heating system in place that does not work. Can you describe it? What sort of floor plan do you have. You mentioned "warren". If you have an old steam or hot water system it may be usable.
Anyone bidding on a heating system really should do a heat loss analysis before they size the equipment. Heating contractors frequently just pick someting nice and big that will certainly heat the house. Then you wind up with something that short cycles because it is way over sized. Make them show you the numbers.