Just because you're paying back your loan doesn't mean that you can't save. Most financial institutions have automatic contribution plans that let you save small amounts regularly. This strategy can really add up over time. Moreover, how you choose to invest your savings will significantly impact how quickly you achieve your goals.
When investing, think about your goals individually. Each goal may have a different time span. For example, you may want to buy a house in 5 years and you may want to retire in 25 years. How you invest for each of these goals will be different.
How long you have to invest, and how much risk you are willing to take to achieve your goals, will both influence how you invest your money.