1. 俗語{ぞくご}
  2. 隠語｛いんご｝
  3. スラング

These are _some_ of the results I got from jisho.org and jpdb.io for the word
"slang".

For example, If I were to say, "dekai is slang for big" in Japanese, how would
I say it?
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question
word-choice words
What's the word for "slang" in Japanese
隠語 means words used when it's considered to be bad using the original words.  
For example, スピード for 覚醒剤, サツ for 警察 (among bad people), 本番 for 性行為.

スラング means words used in a comunity. For example, orz in 2chan, lit in English
speakers.  
If they have important role in the comunity, they should be called 用語.

俗語 means created informal words. For example, キモい, 厨二病, シノラー, ナウい, 徹マン, あけおめ.  
隠語 and スラング are a kind of 俗語.

デカい is too popular among too many Japanese.  
So デカい may not be considered as 俗語, though 俗語 is the best choice.
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answer