They all really can be interchangeable in specific situations, but "I can tell" and "I realize" are relatively more interchangeable with each other and "I know " and "I understand" are relatively more interchangeable with each other.
So, here are their specifically nuanced meanings:
"I can tell" = I can see that
"I realize " = I've come to that conclusion
"I know" = しっています
"I understand" = わかります