Most cyclists use ordinary mountain bikes with off road tyres but never use their bikes in true off road conditions.
I know from experience of commuting on such bikes that a few simple modifications, as follows, will greatly enhance performance. on roads or tracks.
1. Fit smooth (1.5 in or 1.9 in wide) street tyres.
These tyres transform the ease of pedalling and have furthur advantages in lower weight and longer tread wear.
2. Fit alloy pedals (BMX type are ideal)..
Alloy bodied pedals are smoother in operation with less friction, also much more durable.
3. Fit a cartridge type bottom bracket bearing..
The standard BB bearing (crank pin bearing) fitted to low cost bikes is of very poor quality. it reduces pedalling efficiency and on frequently used bikes will rapidly fall apart. A cartridge BB bearing is vastly more robust, much smoother in operation and will last for 10 000 miles or more.
4. Replace a suspension fork with a standard one..
The standard fork is much lighter and wont move during pedalling, especially stand up hill climbing . An alloy fork is lighter still and wont rust.
5. Replace MTB chainrings with single chainrings.
Usually much lighter, certainly much smoother and less hassle .
6. Replace MTB chainrings with Road chainrings.
If you are fit enough - and hate running out of gears, a 52/48 road chainring will increase your road speed .
7. For 700 wheel hybrid bikes - Fit 25c or 28c narrow road tyres to reduce weight and rolling resistance.
If you use your bike exclusivly on roads this modification makes a significant improvement.
NOTE that I have sold most of my new Diamondback hybrid bikes with these tyres See link below.