How to draw a circuit diagram to check a 4 bits number is odd or even
If the least significant bit (lsb) of a binary number is set, that's an odd number. If the lsb is cleared, that's an even number. There's no need for any circuit, just connect the lsb of the input to the output. 

Edit 2 

If you insist on using some kind of chips in your design, you can use inverters and buffers. Here I draw the circuit with two inverters, because that's probably cheaper than using an inverter for EVEN and a buffer for ODD:







simulate this circuit &ndash; Schematic created using CircuitLab

Edit 3 
About your truth table. Yes, if you want a high output for an odd input, just copy the D input column to the output column.

You can then construct a sum of products solution like

(A B C D) + (A B ~C D) + (A ~B C D) + (A ~B ~C D) + ...

But when you simplify it, you'll just get "OUT = D".

Which you could implement with a simple wire. Or with a buffer.