How much of amp can be drawn from an Atmega's output pin..??

Can someone please confirm me that how much of load can be connected to an Atmega's output pin directly..??

Is it fine to connect 3 x 20mA LED in parallel to each output pin of an atmega328.??

No.

40mA is the Absolute maximum the pins are rated for. 20mA is a more sensible limit.

There is also a current limit for the IC as a whole which I think is 200mA through its VCC and GND pins.

40mA per pin with degraded performance above 20mA.

200 mA thru Each Vcc/Gnd pin.
Thus an SMD part with 2 each Vcc & Gnd can hanclle 400mA (and I have previously posted a response from Atmel saying it is 200mA per pin),
while a DIP with just one VCC pin is limited to 200mA. (and AVCC pins do not count as current providing pins.)
The limits on current thru each port in Section 29 notes restrict the total IO current to 300mA total:

  1. Although each I/O port can source more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady state
    conditions (non-transient), the following must be observed:
    ATmega48A/PA/88A/PA/168A/PA/328/P:
    1] The sum of all IOH, for ports C0 - C5, D0- D4, ADC7, RESET should not exceed 150mA.
    2] The sum of all IOH, for ports B0 - B5, D5 - D7, ADC6, XTAL1, XTAL2 should not exceed 150mA.
    If IIOH exceeds the test condition, VOH may exceed the related specification. Pins are not guaranteed to source current
    greater than the listed test condition.
  2. Although each I/O port can sink more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady state
    conditions (non-transient), the following must be observed:
    ATmega48A/PA/88A/PA/168A/PA/328/P:
    1] The sum of all IOL, for ports C0 - C5, ADC7, ADC6 should not exceed 100mA.
    2] The sum of all IOL, for ports B0 - B5, D5 - D7, XTAL1, XTAL2 should not exceed 100mA.
    3] The sum of all IOL, for ports D0 - D4, RESET should not exceed 100mA.
    If IOL exceeds the test condition, VOL may exceed the related specification. Pins are not guaranteed to sink current greater
    than the listed test condition.