How to fix a leaky basement wall from inside?
Yes, don’t we all “prefer clean, simple and effective ways to fix a leaky basement wall.” However, seldom are moisture problems simple. 

First, concrete is porous. It also has cracks and construction joints in it that allows moisture to enter from a zillion different places. 

So moisture is either coming up from below (a rising water table) or its coming from the surrounding ground water in the saturated soil.

If it comes up from a rising water table, it will enter the living space from below through the crack between the foundation wall and slab.

If it comes from the surrounding ground water, it COULD enter the living space through the wall, especially if the exterior side of the foundation wall is not sealed properly.
Either way the moisture enters the living space it will need to be collected and disposed. I think the best way to collect it is on the exterior side of the foundation wall in drainrock and a perforated pipe laid 6”-8” BELOW the interior basement slab.

To keep the subsurface water from seeping through the wall, I recommend installing a moisture barrier on the exterior side of the foundation wall and install a 2” thick plastic mesh on the wall to allow water to flow down to the perforated pipe. If dirt is allowed to be back filled against the wall, the dirt could hold the moisture giving it a chance to seep through the wall.

Once collected it needs to be disposed by extending a solid pipe over an embankment or in a collection well and pumped away.

This may be the most expensive method of solving the problem, but it’s sure to work.

BTW, if you do nothing, you could develop mold (if you haven’t already).