Could someone describe all possible differences which distinguish these three conjunctives ('but', 'however', and 'on the other hand')? For example, are there cases when you can use 'However' but you cannot use 'But' or vice verse? Pedantism is welcomed because I need to know even the slightest nuances. I am also curious if there are any changes in meaning, style, fluency etc. depending on whether 'however' or 'on the other hand' is placed right in the beginning of the sentence or after the subject or the predicate. So far I know from academic grammars that 'On the other hand' can be used to express antithesis, replace an item by a more important one, or signal dissimilar or concessive relationship. 'However' is used only to signal concessive relationship and it is more emphatic than 'But'.
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Comments  (Page 2) 
In my work as a professional editor (Concordia Publishing House), I kept these premises in mind: On the other hand refers to a contrast with only two sides (there are only two hands). But generally reflects a hard exception to a strongly stated case. However is a less strongly stated contradiction.
grammatically horrendous??
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yes, grammatically horrendous.