Using charcoal to clean water
Activated charcoal cleans water mainly by adsorbing the impurities. 

You can also couple normal charcoal with sand and form alternate layers of charcoal and sand and pass water through it. It's a very effective Indian style of filtering water. Nearly all suspended particles gets blocked by the above mentioned filtering style.

You can also convert normal charcoal into activated charcoal to serve your purpose.

Now irradiated water cannot be treated by these methods alone. Normal carbon filtering is used along with several other methods such as ion exchange methods and other such high level water processing methods to treat irradiated water. High levels of radiation can't be treated fully though. 

You can refer to this link to learn about effective radioactive water purification techniques.