Explain how long-term cultivation affects soil organic matter levels?

Constant tilling may grind the soil up fine, aerate it, loosen it up, and make it far easier to hoe and rake (if it's just a garden)  Great for weed control to a degree.  However, over time, the pore spaces between the soil particles become reduced.  Soil compaction becomes increasingly a problem.  This results in poor water infiltration and percolation.  Movement of nutrients toward roots is impeded.  And the roots themselves have to penetrate harder-than-normal soil.  It gets a bit more complicated than that, but one person who has already posted said that exposing underground microbes to tilled soil accelerates organic matter decomposition.  Once the microbes have broken the organic matter down, they have used up their source of food and energy.  Now what might happen is mineralization.  This occurs when microbes wind up absorbing elements such as nitrogen, which they too require.  Now the plants have a nitrogen depletion problem.

Each of the things you mention are different and cultivation would affect each to a different extent.

Cultivation would tend to reduce soil organic matter levels, by turning up the soil and exposing soil organic matter to higher oxygen levels which would accelerate its breakdown into CO2. It's effect on the other soil parameters is more variable. For example bulk density would probably be reduced by the tillage, fertility could increase or decrease depending on how the nutrients in the soil are stored. If they are tied up in organic matter, it would generally increase available nutrients, by allowing the organic matter to break down, making the nutrients available to the plants. 

Tillage can also contribute to wind or water erosion depending on the conditions of the field and weather. 

The main reasons for tillage are planting seeds or seedlings, and weed control. 

Predo,inately, over farming depleats the soil of nutrients which is why in the past farmers allowed field to rest or remain fallow.