Placement of 'Little'

Tennyson writes

It little profits that an idle king...

So your first sentence is not an unheard of construction.

He little helps his friends.

This gives the suggestion that he provides help infrequently. It also sounds formal and literary.

He helps little his friends.

This sentence sounds like he's trying to make his friends smaller.

He helps his friends little.

This sentence could mean infrequently; it also sounds like he's just generally not of much help. It is less formal-sounding too.

This last one, I think we've all agreed, is probably the most common way of expressing what you are trying to say, although gmcgath is right in the comments, where he says that

He helps his friends very little.

is more usual.

Bare little, as an adverb, is uncommon in US speech; it’s been largely replaced by not much.

You will encounter it more often in written discourse of a fairly formal register. There is a distinct preference for placing it immediately before the word it modifies:

• The little-used “little” has been largely replaced by “not much”, OR
• “Little” is little used today, BUT
• ^?”Little” is used little today has a distinct donnish ring even in an academic register. However, as others have noted, very little here is more acceptable.

It’s most comfortably accommodated in sentence-initial or -final position:

• Little as he had helped his friends, they valued his attempt, AND
• Little did he know what awaited him in the following months, AND
• He had helped his friends little; BUT
• ^?He had little helped his friends AND
• ^?He knew little what awaited him in the following months are “literary”.

I suspect that what’s involved in all of these is conflict with the more frequent use of bare little as an adjective or noun, and of a little as an adverb with a slightly different sense. To avoid arresting the flow we have come to shy away from placing bare little in positions where any of these might be in play.