Bwildly:
You probably wouldn't have seen water coming in those holes during a heavy rain storm because it takes time for the rain water to permeate down into the soil to the depth of your weeping tiles. If the water level in your floor drain is below those holes, then check every day after it rains to see if the concrete below the holes but above the water level in the catch basin is wet. That wetness will be water seeping in from the weeping tiles.
I wouldn't be concerned about not beng able to feel a pipe around those holes. Nowadays weeping tiles consist of plastic piping with tiny holes in it. Years ago, it consisted of short (12 inch long or so) pieces of concrete pipe, and the pipes were just laid together end to end, and often not carefully so that you could have gaps between the pipe sections. But, that was good enough to provide a path for excess ground water to drain away by, and thousands of houses were built that way and continue to stand.
Here, let's analyze it this way.
You have holes and you don't know what they're for.
Your house is every bit of 40 years old.
Those holes haven't caused any problem so far.
Why plug them now and risk creating a problem.
So, the logical thing to do is leave them be.
Logic prevails. I win.
PS: The fact that the water level rises significantly in your catch basin when your washing machine spins suggests that the main drain line from your house is partially clogged. I'd say you're better off diverting your attention to having the main drain line from your house cleared than plugging up those holes.
Talk to a plumber. I expect he'll agree with me.
Quattro: The weeping tiles around a house's foundation serve an important purpose. Without them the hydrostatic pressure of the water around the foundation would cause water to want to leak into the foundation. By using weeping tiles to allow excess ground water to drain away, you prevent that from happening.
There are very probably houses that don't have weeping tiles around their basement footings, but I wouldn't call them "well built" houses. If you don't have weeping tiles around your foundation footing, then you probably don't even have insulation on the exterior of your foundation, and that's a recipe for problems. If there's no weeping tiles then the hydrostatic pressure of the water in the ground causes that water to want to seep into your concrete basement walls.
Now, what happens in winter when those same concrete walls are exposed to -40 degree C weather above ground? The concrete looses heat to the atmosphere and the whole concrete foundation gets freezing cold. If there's water in that concrete wall, then it's most likely going to be at the exterior surface, and freezing of that concrete will cause spalling of the concrete wall. That's where the pressure of the ice inside the concrete is so great that it cause the concrete at the exterior surface of the wall to break off in "chips". The more concrete breaks off like this, the more porous and permeable the concrete becomes and the more ground water can penetrate into that wall. So, lack of weeping tiles results in a problem that can best be described as a snowball getting bigger as it rolls downhill.
T