More specifically, if they have the power to wiretap your communications, powerful as in power, not as in strength.
A _____ [powerful] person who holds a menacingly huge amount of power who makes them _____.
This is the 2nd question where I had to disclose that I used Google to research, before asking this question. I searched for "word that means having a lot of power"
The type of scenario you use to describe what you're looking for has powerful cultural resonances. The suggested "Big Brother" (from Orwell's influential Nineteen Eighty-Four) is well recognized amongst native speakers. I've also heard "Stasi" and "KGB" used. They are metaphors, certainly, but widely recognized and gaining currency.
If it is an adjective you are looking for, you can certainly try "Big Brother-like" or "Stasi-like."
Omnipotent -- literally "all-powerful" -- is another adjective, often used to refer to gods.
I don't think there is a single common English word for OP's context. A motorbike or car, for example, might be overpowered or have an overpowered engine, but overpowered people would be people who've been overcome/defeated, not people with too much power.
Not so common, but easily understood in context, is over-empowered.
Note that in practice, the problem OP seeks to highlight normally either reflects a systemic problem (OP's "excessively powerful person" is part of a system lacking appropriate checks and balances), or that person has been overpromoted (he lacks the character attributes that would enable him to exercise his power without raising concerns among the people subject to his decisions and actions).
There are of course a whole host of words to describe people who have and exercise excessive power, but they're normally somewhat "politically loaded". For example, dictator, Fascist, [little] Hitler, authoritarian, despot, overlord, totalitarian, tyrant, etc.
Here are some to choose from: overbearing, domineering, authoritarian, oppressive, autocratic, dictatorial, coercive, imperious, despotic, overweening.
The term godlike is often used to refer to one who seems to have control over anothers destiny.
resembling God or a god in qualities such as power, beauty, or benevolence:
our parents are godlike figures to our childish eyes
SUPPLEMENT: Based on your comment, the word that comes to mind is puppetmaster
a person, group, or country that covertly controls another:
the puppetmaster behind the current administration
Overmighty has a respectable pedigree in precisely this context (one theory of politics holds that a state is constantly in danger from some group of overmighty subjects, whether the army or the bankers), but may be a little out-of-date.
From your example sentence, I'd suggest using influential and formidable or ruthless, respectively.
Though you may also want to save "menacing" and use it elsewhere in your sentence:
They are an influential person who wields a huge amount of power - which makes them a menacingly formidable or ruthless opponent.
The closest word you're looking for is magnipotence:
The quality of being magnipotent; mighty power
and magnipotent:
Possessing great power
Source: OED2
Related to the suggestion of puppetmaster is the word string-puller, which is in my opinion a nice evocative cynical term.
a person who is in control of events or other people’s actions:
Lynch was the main string-puller, nailing the last-minute point that ensured victory
It depends on the context. For instance in video games, the usual term is simply overpowered. Otherwise, you might consider effectively omnipotent, or maybe unstoppable - again, it really does depend on when and why you are using the word.
meglomaniac
A person who is obsessed with their own power.
A person who suffers delusions of their own power or importance.
