Strictly speaking symbols in and of themselves do not have power.
A brief example of a so-called Satanic symbol would be the "dreaded" upside down cross.
Point of fact is that the first time a cross was used in an upside down manner comes right from the bible. Correct me if I'm wrong but I believe it was the apostle Peter who asked to be crucified upside down because he did not feel worthy to be crucified right side up as his Lord and God Jesus had been before him.
This would make the upside down cross a symbol of humility for a Christian person and not the so-called Satanic symbol as has been made popular by popular culture.
In any case symbols are used to evoke beliefs which are generally based on a foundation of knowledge. In and of themselves they have no power.
In addition the root of a symbol might be changed depending upon the era in which it is used.
The swastika has roots in different cultures and is viewed differently by the cultures who use them.
These are just two examples of symbols that may or may not be so-called Satanic.
In some circles the confederate flag is a Satanic symbol.