In extreme conditions it can be matter of several hours. Under good environmental circumstances a person can do without water even for a week. However, the general estimate is about three days.
Sleep deprivation has been a common tool for torture at different times in history. Sleeping is an important part for regeneration. The maximum period to manage without sleep appears to be a maximum of 10 days which in itself is considered severe sleep deprivation and results in lack of concentration. The record was set in 1965 by Randy Gardner who didn´t sleep for 264 hours.
To stay underwater without oxygen is possible for appx. 2 – 4 minutes for an average person. The record was set in 2012 by the Danish freediver Stig Severinsen who held his breath for 22 minutes.
Out of all of these, eating appears to be the least essential because human can stay without food up to about 60 days. The record is 123 days and was set by Charles Robert Ncnabb.