1

The sentence is

てなことで、修行なんてしなくとも、ただ飯を食っているだけで強くなれるんだな。

Google translates first part as "By the way". But I can't find any information how it should be parsed. I think its probably "てな こと で", but only translation of "てな" seems to be this, which doesn't match:

てな; ってな; てね; ってね (prt) (used at end of sentence) (apparently) that's what it's like, isn't it

2

This てな is a highly colloquial variant of という or というような. てなことで is the same as ということで, which in this context means "therefore" or "for this reason", not "by the way".

てなことで、修行なんてしなくとも、ただ飯を食っているだけで強くなれるんだな。
Therefore, even if you don't train, you can get stronger just by eating and spending time.

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