Specifically, do odor removal and air duct cleaning count as tax-deductible home improvements?
In general, for a home you live in, there's maintenance, which is just that, you pay to keep your house in good repair.
There's also real improvements. I spend $xxx to turn my poured cement basement into living space. Here, I keep my receipts and the cost (although not my labor) is added to the basis of my home when I sell.
The couple things that may offer a deduction have to do with energy. When I insulated my basement, there was a state tax credit which I got back when I filed taxes. There are also credits for installing solar panels.
What you've described in your question just sounds like one of the small joys of home ownership.
If the house is not used for business
As noted above but with sources
An improvement materially adds to the value of your home, considerably prolongs its useful life, or adapts it to new uses. You must add the cost of any improvements to the basis of your home. You cannot deduct these costs. Source Page 11, Adjusted Basis, Improvements
A repair keeps your home in an ordinary, efficient operating condition. It does not add to the value of your home or prolong its life. Repairs include repainting your home inside or outside, fixing your gutters or floors, fixing leaks or plastering, and replacing broken window panes. You cannot deduct repair costs and generally cannot add them to the basis of your home. Source Page 12, Adjusted Basis, Repairs versus improvements
But this is different if you are a lessor.
Generally, an expense for repairing or maintaining your rental property may be deducted if you are not required to capitalize the expense.
You must capitalize any expense you pay to improve your rental property. An expense is for an improvement if it results in a betterment to your property, restores your property, or adapts your property to a new or different use. Source Page 5, Repairs and Improvements
Home Improvements that improve the home's Energy Efficiency are currently eligible for federal tax credits.
This includes renewable energy equipment (solar panels, etc.) and Nonbusiness Energy Property Tax Credit. The credit is 30% of the cost.
Equipment and materials can qualify for the Nonbusiness Energy Property Credit only if they meet technical efficiency standards set by the Department of Energy. The manufacturer can tell you whether a particular item meets those standards. For this credit, the IRS distinguishes between two kinds of upgrades.
The first is "qualified energy efficiency improvements," and it includes the following:
•Exterior windows and skylights
•Certain roofing materials
The second category is "residential energy property costs." It includes:
•Electric heat pumps
•Electric heat pump water heaters
•Central air conditioning systems
•Natural gas, propane or oil waterheaters
•Stoves that use biomass fuel
•Natural gas, propane or oil furnaces
•Natural gas, propane or oil hot water boilers
•Advanced circulating fans for natural gas, propane or oil furnaces