Jesse,

Don't fret!  There are tons of options that are great.  And don't hold out: radiant flooring IS a possibility.  Let's talk....

But Umbra's summary is right on.  

I'm going to the permit office tomorrow to see if I can get my radiant floor design approved.  This is on a 72-year-old house.  The secret is: you can remove your ceilings, they're not structural members of the house.  It's messy and ugly, but in the end you'll have more efficient, more comfortable heat.  I hope.

As for insulation, windows and doors are a no brainer.  Also consider slow rise foam for your exterior walls - imagine having R-30 walls.  That's a lot of heat (or cool air) saved.

The best energy is the one you don´t use!

If you buy a new heat generation system first, it will be oversized in the future, after you insulate your house. Oversized equipment is always less efficient than one sized correctly. So you would overpay twice: for a too large system and for comsumption of energy that is higher than needed (because of the lower efficiency) over the whole lifetime of the new equipment!

As Umbra wrote, the number of options are very large, so it´s best to invest some money hiring a specialized consultant who will make you a complete project, starting with the reduction of demand, which will consist mostly of insulation measures.

You should also ask around and search the Internet for possible financial asssistance and/or subsidies to do a complete energy savings project.

Have fun!

I was surprised not to see geothermal heat pumps mentioned. We are in the process of installing one at our house on the grounds that (if the EPA is to be believed) they are the most efficient system in the overall use of external energy sources.

That is, if I compare the amount of oil I would use in my oil furnace with the amount of oil the utility would use to make enough electricity for my heat pump,  the utility will use less.

Incidentally, my preconception was that we could
not drill the wells because of being in the city,
but I was wrong.

I understand the problem that electrical generation can be noxious, but that is a separate battle for all of us to fight with the utility companies and the government.

Back Puffing on an oil fired furnace or boiler is a "Surefire" indicator of a lack of air to the combustion system. You need a supply of Combustion Air as long as you keep this working in your home. This is a big safety concern and needs to be addressed right away! Call a Heating Contractor NOW!

Any new equipment you get should be of a direct vent design, providing a direct supply of combustion air from the outside into the combustion chamber, and a direct exhaust to the exterior. In both cases two or three inch PVC pipe can be used for venting.

When deciding on upgrading your heating system (You will want to move from the steam boiler as you will not want to tolerate the low efficiency with the peak efficiency available now and in the future being only about 83%) you will need to have the distribution system assessed for possible conversion to hot water.

If you have a single pipe steam system, then it is total replacement time!

Replacement of everything is not always needed. If you have a two pipe steam system then a possible conversion including a reworking of the existing radiators is possible.

You may have to replace the piping and this can be done with pex type piping , the same used for infloor radiant heat. This can be run through the interior of walls to the radiator locations with out as much destruction as one might think.

I like radiators as you can get better zone control with little perks like a radiator for a bathroom that also serves as a towel warmer! You can keep the bathroom cooler with a warm towel to dry with!

A new boiler can also be used to heat your tap water and Solar can be added to this  as well.

geothermal heat pumps are not always the greenest option.  I can only speak to cold climate conditions.
When I say cold, not that mamby pamby stuff of 10 or 15, rather -15 to -30.

Efficiency in the building reducing the need to heat and cool is the BEST investment.

depending on your fuel mix and Location  chances are the high efficiency gas heating equipment will end up with a net lower greenhouse gas emissions than a ground source heat pump as well as provide a better return in investment.

I speak as oil burner owner, hot-water baseboard.
That's it--then compare alternatives

If you have a underground oil tank I would have it removed first.  If it leaks it going to cost a lot of money.

Your story reminded me of the experience close friends had with an unexpected leak.  My advice is check your attic as well as your basement. Unforeseen surprises may await you in unexpected places.

I'm surprised that no one has mentioned a solar (thermal) hot water system as a solution for Jesse.

A solar system with an adequately sized storage tank, placed in the basement, could meet not only his heating needs but also provide his domestic hot water (and heat his hot-tub to boot).

If he "backed up" his solar thermal system with a Bosch or Takagi variable flame tankless water heater, which are very efficient, he'd be "greening up" on several fronts AND solving his boiler problem.