In this context, the Wain (which means wagon) is a constellation.  It is not mentioned in either The Lord of the Rings or in The Silmarillion.

• 10.006 where the stars of the Wain were already twinkling,

I imagine that Wargs are terrible genetic and magical experiments on wolves, as were Orcs to Elves, Trolls to Ents.

• 06.059 But even the wild Wargs
• 06.060 in the dreadful language of the Wargs.
• 06.060 and then all the Wargs
• 06.061 The Wargs
• 06.061 Then they often got the Wargs to help
• 06.061 The Wargs had come to meet the goblins
• 06.062 and even the Wargs dared not attack them
• 06.063 The Wargs were angry
• 06.063 So the Wargs had no intention of going away
• 06.067 and looked down upon the ring of the Wargs,
• 06.070 All round the clearing of the Wargs fire was leaping.
• 07.117 with the Wargs
• 07.118 if he leads all the Wargs
• 07.121 Not eaten up by Wargs or goblins or wicked bears yet I see’ ;
• 07.122 he had caught a Warg
• 07.122 with Wargs for the dwarves,
• 07.124 and the Warg?’
• 07.131 and Wargs run swifter than ponies.
• 17.041 and Wargs are
• 17.054 There a host of Wargs came ravening
• 17.058 The Wargs were scattered
• 18.051 and the Wargs had vanished from the woods,

What an evocative, delicious, elegantly simple name.  It makes me want to be bewildered.  I include here references to “the Wild” as a location – or perhaps a state of being.  I look forward to the day when I can expand the concordance to include “wild” in its own right – it is used beautifully in this work.

• 03.003 before we can come into Wilderland beyond.
• 06.050 over the Edge of the Wild on the borders of the unknown.
• 06.059 (for so the evil wolves over the Edge of the Wild were named)
• 07.151 Remember you are over the Edge of the Wild now,
• 18.051 The Wild was still the Wild,