Fallout 2 did take itself seriously, with ironic humour thrown in for good measure. The amount of references to pop culture did detract from the overall product, but did not diminish the themes tackled in the game.
It's interesting to see people cling to the humour in Fallout 2 (which the developers admitted was too much and scaled it back in Fallout: New Vegas), while missing the bigger picture. The bigger picture that includes the political rivalry between New Reno, the NCR, and Vault City for control over North California. The deliciously complex political situation in Redding. The competition between the families of New Reno. The man/mutant struggle in Broken Hills. Gecko and Vault City. Modoc and the Slags. But no, people continue to go "HEY FALLOUT 2 HAS (insert pop cultural reference) SO IT'S FINE FOR FALLOUT 3 TO MAKE NO SENSE."
The same goes for Old World Blues. Yes, it is superficially comical. But...