Situational irony: Quilp’s death
Quilp has a direct hand in evicting Nell and her grandfather but he did not realize his actions towards them would result in his own death.
Situational Irony: Nell’s death
The initially reason Nell’s grandfather got into gambling and fell into a loan with Quilp was to save her, but actually his actions only resulted in their eventual demise.
Dramatic irony: Frederick’s greed
Frederick is so far gone in his quest for his grandfather’s wealth, but the reader knows this is not the case, and that Nell and her grandfather are actually living in poverty as beggars.