If I have a power shortage can I close the Breaker to my oil burner, tap into the power switch that turns the boiler on & off and plug it into my gas generator for heat & hot water ?

Yes

You should not merely "tap" into it, you need to disconnect the wires which go to the breaker. That eliminates any chance of backfeeding should you turn the breaker.

The OP's post is unclear. Do not under any circumstances make it possible in any way shape or form to connect utility and generator power at the same time accidentally. Use an approved transfer switch or interlock kit.

Utility company's frown upon unapproved connections especially when a worker can end up dead.

See post #7 here: https://www.askmehelpdesk.com/electrical-lighting/combining-generator-outlets-advisable-even-possible-458891.html

NO. Only an approved interlock kit or a transfer switch can be used.

Interlock kits MAKE SURE that both breakers have to be off, before only one is allowed to turn on.

Transfer switches are DPDT switches, but interlocked so both contacts cannot engage when they fail.

Two breakers without a interlock kit ALLOW both to be on. When there is no power, the chances that it can accidentally be thrown increases. There cannot be ANY margin of error.

KISS's statements are absolutely true. If you wish to pursue this, take the extra steps to assure the safety of your family AND the utility worker(s) trying to restore power. You could be held liable if someone is injured (or worse).

The bottom line is this: it will probably work if the generator has sufficient capacity, but it is dangerous. Without a proper transfer switch, the potential for electrocution and/or fire exists. Sorry if this isn't what you want to hear, but it's true.