Why did the Wraith try to activate the mass cloning device after the defeat of the Replicators in Pegasus? Sheppard asks this but Todd's answer makes no sense. During the war with the Replicators, they might not have lived for very long so food might not have been such an issue, but after the war, it seems nigh-suicidal. Simply because they couldn't use it during the war doesn't make it any less of a spectacularly dumb idea now.
Long story short, Todd wanted a clone army and stole the Asuran ZPMs to power the facility.
The cloning facility was not new, nor was it based on Replicator technology. In fact, the cloning lab was the key to the Wraiths' defeat of the Ancients 10,000 years ago. As mentioned several times during the show, Ancient technology is far more advanced than the Wraith equivalent, and the Wraiths won the first war largely only because of their numbers.
These numbers did not exist at the beginning of the war, and one of the things that cost the Ancients victory was that they did not understand how the Wraith kept replenishing their numbers despite heavy losses. Many of the Ancient experiments we see during the show - including the Pegasus replicators - were a desperate attempt to balance that disadvantage.
Todd addresses this very issue in the episode you're referring to (S03E05 "Spoils of War"):
TODD: Within weeks, our army had grown to hundreds of times its original size. From that point on, the tide of war turned in our favor and there was nothing the Lanteans could do.
One of the original Wraith commanders during the war, Todd was apparently one of the few remaining ones who knew of the lab's existence. The facility itself was using the existing Wraith method of reproduction (a queen laying "eggs"), but the process itself was sped up a thousand times by introducing Ancient technology to supply the energy instead of the queen. The original ZPMs had been depleted, so Todd needed new ones to power the facility. He took advantage of the confusion on Asura to steal three so that he could reactivate it. He was betrayed, however, by the Queen of the hive ship he was working with.
As for WHY either of them wanted more Wraith around, they probably assumed that they would cross that bridge when they got there. The first priority was to build an army so that they could overwhelm the other Wraith factions and win the civil war. They most likely planned to overrun Atlantis after that, which would give them Earth as a new feeding ground.
To activate the facility required a ZPM or an equally powerful energy source the Wraith did not have access to until Todd stole a few during the attack on the Replicator planet.
After the Replicators were defeated, the Wraith were still in the same position all the hives were awake and there were not enough humans to eat.
The cloning facility is kind of a dumb idea unless you consider that the Wraith can feed on each other, millions of clones for your army allowing you to overwhelm the other hives with pure numbers and a walking larder actually makes it a pretty decent plan.