Are there any strategies that could reduce the threat that the world's population may eventually not be able to sustain itself and its environment?

The issue you are concerned about was actually first raised by the English clergyman, the Reverend Thomas Malthus, who noted in the late eighteenth century that the population was growing geometrically but food supplies were only growing arithmetically, and predicted this would eventually lead to a crisis in which food supplies were inadequate to feed the world population. There are two possible solutions to this problem: reducing population or reducing the environmental impact of each person.
There are several ways to reduce the population. The first is government incentives ranging from the authoritarian (China's one-child policies) to various more subtle incentives, such as eliminating tax breaks and other forms of subsidies for bearing children and increased incentives or tax breaks for not having children. Access to free birth control, abortion, and sterilization also allows people to choose not to have children. Another major step in reducing population growth is educating women, increasing gender equality, and reducing poverty, as better-educated women in countries with less poverty and more equality of opportunity tend to bear fewer children.
There are several ways to reduce the environmental impact of individuals, including recycling, using renewable energies, reducing use of fossil fuels, and implementing other green initiatives. There are several strategies to increase agricultural yields in a sustainable fashion. One of the most obvious ways to increase food supply is for people to follow vegetarian diets, as it takes 8 to 30 pounds of plant food to create a pound of meat; it is much more efficient for people simply to eat plants rather than feed plants to animals and then eat animals.