OK, let's give this a go.
- "challwa" appears so much in all the sentences that it must mean something like "fish"
- "challwataxa" appears exactly once in each sentence, so it probably means something like "I caught" (the verb for catching a fish being cognate with the word for fish)
- "hach'a" appears in exactly three sentences, so it could mean the large fish
- my vague memories from when I learned some of the Aymara language years ago1 tell me that "paya" and "kimsa" are numbers, probably two and three.
Now let's have a look at some of the statements. The simplest is:
- "Paya challwallawa challwataxa."
Going with all my deductions/guesses from above, this must mean "I caught two [type] fish". Assuming this speaker isn't the liar, we have 5 = d and that "challwallawa" means the smallest type of fish.
The word "challwalla" appears as well as "challwallawa"; these are so similar that they must be related, and I'll guess that "challwallawa" is the plural of "challwalla". Which means ...
- “Mä challwalla paya challwampiwa challwataxa.”
"Mä" must mean the number one, and this sentence means "I caught one small fish and two [type] fish". Again assuming this speaker isn't the liar, we have 6=f and that "challwampiwa" means the medium-sized type of fish.
- “Mä hach’a challwawa challwataxa.”
We know this means "I caught one [something] fish", so presumably "hach'a" means the largest type of fish and 1=g.
- “Kimsa hach’a challwawa challwataxa.”
This means "I caught three large fish", so we've found the liar. (It's also not surprising that the liar's claim is the most exaggerated.)
- “Mä challwa mä hach’a challwampiwa challwataxa.”
This sounds like "I caught one fish and one large fish" - I guess it means 3=a.
- “Mä hach’a challwa kimsa challwallampiwa challwataxa.”
This means "I caught one large fish and three small fish", so 4=c.
- “Kimsa challwa paya challwallampiwa challwataxa.”
This sounds like "I caught three fish and two small fish" - I guess it means 7=e.
By elimination, we have the final solution:
1 = g
2 = b (liar)
3 = a
4 = c
5 = d
6 = f
7 = e.
1 Yes, really.