How to make my gas heat less noisy?

As "Patriot Says" first stop is to check to see if the filter(s) clogged......then if there are any vent or duct dampers closed that would make noise. Sooooo: does your blower motor have speed adjustments - - - if not, is it worth changing the blower & controls?

Does it seem that the air coming out of the vents is at too great a velocity? Does your system include air conditioning? . . . . I ask because older forced air furnaces had one-speed motors. With air conditioning, they used two speed motors - the higher speed for use when cooling. At most, speed was adjusted by using belt drive and using different sized pulleys to find the appropriate speed. Newer systems use solid-state controls and multi-speed fan motors: the newest/best have computer selected speeds with the control adjusting fan speed to meet demand.....others have multiple fan speeds that can be set manually: example - our 5 year old Lennox has 6 speeds to select for heating.......6 speeds to choose from for cooling....plus a "-15%" control on all plus a super-low speed when setting the fan to continuous run.........you more or less set the lowest speed that gives adequate heating or cooling.

Check the filter as it may be clogged and the fan is having to work hard to get the air flow that it needs. Make sure all vents are at least 1/2 open, also as the air is being pushed through the duct and if there is resistance to the push, it can be "whooshing." If the system has the old registers with the handle and notches, make sure they are open wide. These had a tendency to have air rush around them and push on the back of the vent and that made noises, too.

One of two possibilities, a) either the filter is dirty reducing the air flow, or b) the system fan motor was changed and a faster motor was installed creating too much air flow. Part of the system design is to match the duct size to the blower air volume so as to minimize noise. Building codes go into detail in Manual D about the maximum velocity through ducts and vents to prevent air noise. Does this sound like the more likely possibility?

Insufficient area for return ducts may make a forced air heating system noisy. Increasing the size calls for carpentry and may be simple or complex and expensive.

http://inspectapedia.com/aircond/Return_Ducts_Too_...

After checking basic things like filters and dampers have a hvac contractor check the static pressure in the ducts. Some simple math and some simple tools like a incline manometer will tell the story.

I don't think you can fix it because it's not broken. That's why they call it a forced air system.