I think you must follow some literature related to polyurethane because they also behave the same way as you described about Poly-2-ethyl-2-Oxazoline.

Why did you add PVA (polyvinyl alcohol) ?  PVA is brittle, so it doesn't help to improve flexibility (reduce brittleness of Poly-2-ethyl-2-Oxazoline). I believe it works for PEG of Mw 400 or 600 of 15 - 20 wt %.

Drying temperature and humidity may also contribute to the resulting films. You may try to dry at room temperature at 50 %RH

I agree with Kairuddin but, to be more precise; you should focused on the molecular weight (or DP) of the additive polymer in your blend. Even may be the tacticity.  

Water acts as a plasticizer, so drying causes glass transition into a glassy state. You need another platicizer than water, a plasticizer that does not evaporate upon drying

I think your polymer has low Tg due to less crystalline chains and you are adding PVA and PEG which will increase the chain mobility which will make your system more sticky. Check the purity of your polymer and molecular wt of polymer. I think you are getting low molecular wt polymer.  

Also in order to form the film you need to check the inherent viscosity values of your polymer (must be bigger than 0.5g/dL) 

Poly(2-ethyl-2-oxazoline) is hygroscopic so as has been already mentioned will be plasticised by water under normal ambient conditions. The amide group in the polymer can also form hydrogen-bonded complexes with other polymers (e.g. PVA, or PEG if the amide group is protonated), so you might still expect a brittle polymer for this reason with a dry blend of these polymers.

So can anyone suggest me how to make it non sticky,am planning to use it for wound dressing and later drug delivery

Stickiness probably arises from hydrogen bonding and wetting properties. If synthesising different polymers or co-polymers is not an option then a possible strategy could be to look for plasticisers or other materials to blend with to make the material more hydrophobic?

PEOZ and PEG and PVA are very hydrophilic polymers and are able to absorb substantial quantities of water from moistured air. Placticizing effect of water (formation many (H2O)n bridges between polymer macrochains) onto the polymers make them very sticky. Otherwise drying the polymer blend eleminate (H2)n bridges between macrochains that allowed to form strong hydrogen bonds between functional groups of polymer constituents. It makes PEOZ/PEG/PVA blend very brittle. Good luck.

Dear Tolstov,

I am planning to cross link PEOZ with cellulose,will that be of any help?

This is a ternary system, and the system by itself is complicated. I am not sure about your goal. However, i would say before approaching toward a complicated ternary systems, it would be useful to make binary blends of PEOZ/PEG and PEOZ/PVA. Determine the Tg of both systems treated at room temperature and at vacuum dried. This will help you to understand the which is inducing more mobility to the matrix. 

The presence of free polar groups at the outer surface of the film and hydrophilicity of the side groups contributed to the sticky problem. Free radical crosslinking could be useful to reduce the surface charge.