If you notice none of the described symptoms when you plug the laptop adapter directly into the wall outlet then you should consider discontinuing the use of this surge protector / plug strip. This seems to me to be a serious safety issue that needs to be addressed immediately.
Once you get back to a safe usage scenario you should do some checking of the laptop adapter for safety issues as well. Remove the adapter from the wall power and from the laptop. Now using a digital multimeter in the resistance (ohms) measuring mode check for any low resistance readings (less than 10 megohms level) between any of the AC power leads and any of the contacts at the laptop charger plug end. If you find any low resistance connections from the AC to DC side of the adapter then you should replace that as well.
(Note that all of the numerous laptop adapters I have encountered are supposed to be 100% isolated from input to output. I.e. NO input to output electrical connection).
Now back to your surge protector. Some surge protectors may have installed components such as MOVs or high voltage capacitors between the AC lines (hot and neutral) and the earth ground connection of the AC wiring coming into the protector. If they are wired this way it is possible for some people to feel a slight shock when touching any grounded metal parts of equipment that is plugged into the downwind power jacks of the surge protector. In my electrical engineering opinion I do not think this type of surge protection wiring is the best idea. Now at the same time some manufacturer of a surge protector may boast that their unit is superior (and thus way more costly) if it has MOVs attached line-neutral, line-earth, and neutral-earth. This can lead to low level leakage currents from the AC line to the earth ground connection. If your "high end" unit is like this you should consider not using it!
If your laptop adapter has a connection from its input AC leads to DC output side and it is used in conjunction with a surge protector that has multi-MOVs causing leakage currents to flow then this can lead to the slight shocks that you feel when touching metal parts of the laptop.
My recommendation - safety first when dealing with anything electrical attached to the AC power lines. At first indication that there is something amiss discontinue use immediately.
According to howstuffworks.com the most common type of surge protectors contain a metal oxide varistor or a gas discharge arrestor that utilizes the grounding wire to divert extra current.
However, as others have commented, the neutral wire is usually also used in conjunction with the ground, and therefore, you should get some, but not full protection when bypassing the 3rd prong.
That said, it's never considered safe to use bypass the 3rd prong (even with 2 to 3 prong adapters) and it is likely your insurance / the manufactures insurance will not cover damages caused as a result of such use.
Best Answer
The "don't put a surge protector on a surge protector" rule is not about the surge protection, it is about overloading circuits and tripping over wires - which really doesn't apply here. I would treat the installed receptacles as "ordinary" and use a surge protector (of known quality) to add more receptacles.