These terms are not so easy to understand.But usually a paradox is a contradiction.IT is something that is the opposite of what we might think "an apparently true statement or group of statements that leads to a contradiction or a situation which defies intuition."
For example you might think that the harder you work, the quicker your work will be done,but paradoxically,the opposite is the case.You need to take a break and relax,and then your work will get done quicker.
Irony is something used in literature "a literary or rhetorical device in which there is a gap or incongruity between what a speaker or a writer says, and what is generally understood".
For example it is ironic if you take a car to get somewhere quicker and then you get stuck in traffic and end up arriving later than if you had taken the bus.
These things are really hard to explain.When you see examples in texts you read,you can understand them better.