Fromer frofessional Lurker here: First up http://jgram.org/ is a superb website for looking up grammar constructions. In combination with the infamous https://jisho.org/ lots of stuff can be found 
Now to the translation. Copying @fernie s format, because I like it, thanks! Old Version, Page 7 (puns incoming!):
-
Panel
前 - before, last time
は - topic marker
いっぱい - a lot, much, completely filled
入れた - 入れる (in -た [past] form)
=> 前はいっぱい入れた - Last time you put in a lot [of sugar]. -
Panel
無糖 - unsweetened, sugarless
派 - faction, group, party
に - target particle
なった - なりました - to become, to change into
ん - の - possessive/genitive particle (Here adding an explanatory tone)
だ - です - copula
=> 無糖派になったんだ - I joined the sugarless party -
Panel
それは無党派 - That is a political independent voter -
Panel
それは武闘派 - That is armed struggle faction (?) That does not really fit the panel imho… -
Panel
それは未踏派 - That is travelling on foot [through the] unexplored. Or more liberal: That is exploring uncharted terrain/That is exploring remote areas. Probably a pun on the combination of:
未踏 - unexplored
踏破 - travelling on foot/all over -
Panel
それはカメハメハ - That is Kamehameha [First ruler of Hawaii] -
Panel
ダイエット - diet
してる - している - しています - progressive form of する
から - therefore, (inverse because)
お - 御 - honorific
砂糖 - Sugar
は - topic marker
控えてる - 控えています - to hold back, to abstain
ん - の - possessive/genitive particle (Here adding an explanatory tone)
だい - かい - か - casual question marker or weak exclamation
=> ダイエットしてるからお砂糖は控えてるんだい - I am abstaining from sugar because I am dieting. (Going with the “weak exclamation” of -だい)
Comments welcome
I hope someone finds this helpful 
EDIT: Added to the の explanation. Thanks to @theghostofdenzo for reminding me.
EDIT2: Added a remark for the 5th Panel on the combined word. Thanks @Wiggle for pointing it out.