(Asker's comments: the Doctor mentions that Strax gave his life at one point but was then brought back. I don't understand. Was there an episode I missed or something? And how did the lizard lady, Madame Vastra from the Dawn of Time, get to Victorian England? And how do all these characters connect to the Doctor? I know where Madame Vastra and Strax come from (what species they are/the episodes they would've/should've premiered in), but I don't understand who the characters are and what their connection is to the Doctor. I can't recall specifically seeing these exact three, named characters prior to the "Devil's Run" conflict. I think I would've remembered a lizard lady who is married to her maid. Just saying.)
Vastra, Jenny, and Strax all debuted in "A Good Man Goes to War". Their relationships with the Doctor are touched upon later, but mostly they are just people that he has helped throughout his adventures. You did not miss an episode, but as for how they got to Victorian England after the events of Demon's Run, the Doctor told River at the end of "A Good Man Goes to War" to take everyone home (as she had a vortex manipulator in her possession). However, there was a minisode called "The Battle of Demons Run: Two Days Later" which took place after the end of "A Good Man Goes to War" but before "The Snowmen", and it shows Vastra and Jenny reviving Strax, who had "given his life" in the battle against the Headless Monks at Demons Run (which is what the Doctor was referring to when he said "he gave his life for a friend of mine (likely Amy, since the point of the battle was to rescue her); another brought him back"). And lastly, Vastra got to Victorian Englad simply by being a Silurian, who have extended lifespans as well as stasis chambers that they can use to hibernate. Vastra was awoken from her slumber by contruction in the London Underground and attempted to exact revenge for her sisters on the workers, but the Doctor convinved her to show mercy. This was revealed in "A Good Man Goes to War".