Re: Strong and weak nuclear forces.

Since this is a very basic and fundamental question, I'll try and provide
the following overview which does not go into terrible detail about
higher-level subjects such as quantum mechanics:
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Protons in the nucleus do, in fact, repel due to their positive charges. 
Without delving too deeply into the subject, the strong nuclear force that
particles in the nucleus feel attracted to each other by is over a hundred
times as strong as the electromagnetic force repelling them!  So the
protons are tightly bound into a small volume in the nucleus.  If a typical
atom were the size of a football field, the nucleus would be about the size
of a grape seed.  So there's a force pushing the protons out, but another
stronger force holding them tightly together.  This force, however, has a
very short range, it only acts over extremely short distances.  The
electric field of the protons extends far outside the nucleus, binding the
electrons to it in orbitals. 

To answer your question, the electrons are also partly inside the nucleus!
 Electrons are far lighter than protons, and are only bound to the nucleus
by the electrostatic force attracting them to the protons...the electrons
also repel each other!  The real quantum mechanical picture is a little
fuzzier than that, but you can think of the electrons as existing in a
cloud around the nucleus.  An electron doesn't just sit at some single
point in space, we know from quantum mechanics that it fills an area known
as its orbital.  The electrons repel each other in their orbitals, so they
stay as far from each other as they can, but they're still all attracted to
the positively charged nucleus, so they still fill a space as close to it
as possible.  Part of the electron orbital does, in fact, exist inside the
nucleus!  The electrons exist in a balance of attraction to the nucleus and
repulsion from each other.  The electron orbitals fill almost all the space
that the atom really occupies, and they determine the atom's shape and all
of its chemical properties.

The weak nuclear force is something else again, and is related to the
electromagnetic force.  It is responsible for radioactive decay when the
number of protons and neutrons in the nucleus is out of balance according
to the rules of quantum mechanics.  This force causes conversion between
protons and neutrons via the production of other subatomic particles,
leading the nucleus back to a stable state.