In some ways, the American colonists felt that the British were oppressing them because the British actually were doing so. One example of this would be the Massachusetts Government Act, in which the British essentially took away any right of self-government from the people of the various towns in that colony and gave the governor (appointed by the British) the right to take complete control. It is not hard to see this as an act of oppression.
In another way, the American colonists felt that the British were oppressing them because the British were acting differently than they had been in previous times. Before the French and Indian War, the British had more or less left the colonists alone. They had not really taxed the colonists much and they had not strictly enforced their laws about things like trade. The Americans had gotten used to being left to rule themselves. When the British took more control, the Americans felt oppressed even though what the British were doing (taxing, enforcing laws) was not really all that oppressive.
These were the main reasons for which the American colonists felt oppressed in the years leading up to the Revolution.
The reasons the colonists felt they were being oppressed had a lot to do with Britian not giving them the rights they felt they deserved. It started with the French and Indian War which lasted from 1754 to 1763, where Britain ran up a debt fighting the French. In order to make money, Britain began imposing taxes on the colonists, as they felt the war was done to protect them. Immediately following the end of the war, multiple acts were passed to charge the colonists, such as the Sugar Act of 1764 and the Stamp Act of 1765. Though the taxes were just a small fraction of what those in Britain had to pay, it still angered the colonists. As the colonies and their motherland were separated by an ocean, the colonies had, in a sense, started to develop a feeling of autonomy, and the taxes invaded that.
What really annoyed colonists was the idea of "no taxation without representation." Because they had no representation in Parliament, they felt it was a violation of their rights as Englishmen to then be taxed. Events later on would increase the tension between sides and lead to the colonists feeling they were oppressed. Reacting to the Tea Act, colonists expressed their discontent by dumping tea in the Boston Harbor in the Boston Tea Party. This led to the Crown trying to punish the colonies as means of reasserting their power. They passed the Intolerble Acts, which included closing the Boston Port and allowing British soldiers to stay in the homes of colonists. All this could be considered further oppression of the colonists because it limited their freedom ever so slightly.
The presence of military force also gave the colonists a sense that they were being threatened. Between the Boston Massacre and the Quartering Act, the British soldiers were receiving a good amount of attention. It is the presence of the military that Patrick Henry mentions in his speech in the Virginia Convention in 1775 for why he believes war is inevitable and action must be taken.