When you cast Maelstrom Wanderer, the stack will be:
Cascade
Cascade
Maelstrom Wanderer
You resolve the cascade trigger on the top of the stack, and reveal Duneblast, and may cast it. Duneblast resolves if cast. Then you resolve the next cascade trigger, and reveal birds, and may cast it. Birds resolves if cast. Finally Maelstrom Wanderer will resolve.
Each cascade ability will get to resolve separately (C.R. 116.4, 702.84a). Thus when the first cascade ability that resolves this way resolves, if you cast Duneblast with cascade, Duneblast will go on the stack above the other cascade ability, if any (C.R. 405.2), and get to resolve before that ability (C.R. 116.4) — thus whatever card you cast due to the other cascade ability won't be affected by Duneblast.
I cast Maelstrom Wanderer
On first cascade I hit Duneblast
Second Cascade I hit Birds of Paradise
Does duneblast resolve first and I get to keep the birds?
BGGRock
Modern
BRGJund
BBGRock
When you cast Maelstrom Wanderer, the stack will be:
Cascade
Cascade
Maelstrom Wanderer
You resolve the cascade trigger on the top of the stack, and reveal Duneblast, and may cast it. Duneblast resolves if cast. Then you resolve the next cascade trigger, and reveal birds, and may cast it. Birds resolves if cast. Finally Maelstrom Wanderer will resolve.
[180 classic cube]
EDIT (Feb. 16, 2021): Add rule citation.