Why do the osmoles of urea when they pass into the cell exert an osmotic effect and draw water into the cell, while when they were outside they had no effect?
Urea freely crosses the cell membrane, therefore independent of the osmolarity of the solution, it cannot build up a gradient of osmotic pressure across the cell membrane - The extracellular urea concentration will quickly equilibrate and build up a similar intracellular concentration.
Urea, also known as carbamide, is the carbonic acid diamide. In the urea cycle, two ammonia molecules (NH₃) are combined with a carbon dioxide (CO₂) molecule to produce UREA. It is neither acidic nor basic when dissolved in water. Urea is practically non-toxic (LD50 is 15 g/kg for rats). https://en.wikipedia.org/wiki/Urea
Urea in concentrations up to 10 M is a powerful protein denaturant as it disrupts the noncovalent bonds in the proteins. This property can be exploited to increase the solubility of some proteins.