Directions to Langelinie from Copenhagen Airport:

Trains leave every 20 minutes from the arrival hall in Terminal 3 to Østerport Station (located 2 stops past Copenhagen Central Station). Outside Østerport Station, bus 26 to Langelinie Pier departs every 20 minutes and takes approximately five minutes. The total trip will cost about DKK 25 (EUR 4).
You can also take the Metro/subway from the airport to Kongens Nytorv Station and catch bus 26 from there.

Bus 26 does not operate during the week-ends, but it is possible to walk from Østerport Station to Langelinie Pier:

Time required : Train to Østerport Station: 20 minutes
Bus 26 from Østerport Station : 5 minutes (plus up to 20 minutes wait).

Directions to Freeport from Copenhagen Airport:
Trains leave every 20 minutes from the arrival hall in Terminal 3 to Copenhagen Central Station.
A taxi from Central Station to the Freeport Terminal will take approximately 10-15 minutes and cost DKK 75 (EUR 10).

Time required : Train to Central Station: 20 minutes
Taxi: 15 minutes

Luggage storage in Copenhagen:
Luggage storage is available at Copenhagen's Central train station at a cost of 45 Kroner/item. This staffed office is located at the extreme right corner as you enter thru the main entrance. Lockers are also available.

External resources:
Copenhagen map (inludes cruise port locations)
Cruise port website