Physicist could answer this far better than I; but here goes:
THE STANDARD MODEL:
The best description of how matter and energy interact (sans gravity) is called “The Standard Model” It describes the organization of all of the particles and how they interact. The elementary particles are divided into two families called quarks and leptons. Each family consists of six particles and three of each particles in each group are acted on by a force carrier.
Quarks: Six called, up charm, top, down, strange, and bottom.
Up, charm, and top use the gluon for their force carrier.
Down, strange, and bottom use the photon for their force carrier.
Leptons: Six called: e neutrino, u neutrino, t neutrino, electron, muon, and tau.
E neutrino, u neutrino, and t neutrino use the W boson for their force carrier.
Electron, muon, and tau use the Z boson for their force carrier.
Gravity is not included in the standard model, however it is believed that is exchange force is a graviton.
THE FOUR FUNDEMENTAL FORCES OF NATURE:
The four fundamental forces in nature:
Strong force
Weak force
Electromagnetism (EM)
Gravity
All of the fundamental forces are considered Exchange Forces. In other words the force involves an exchange of one or more particles.
The exchange particles are as follows:
Strong – The pion (and others)
Electromagnetic (EM) – The photon
Weak – The W and Z
Gravity – The graviton
The Strong Force:
It is a force that holds the nucleus together against the repulsion of the Protons. It is not an inverse square force like EM and has a very short range. It is the strongest of the fundamental forces.
The Weak Force:
The weak force is the force that induces beta decay via interaction with neutrinos. Not only would the Sun not burn without this force A star can “burn” by a nuclear fusion process. Three of those processes are proton-to proton fusion, helium fusion, and the carbon cycle. Here is an example of proton-to-proton fusion, which is the process our own sun uses: (two protons fuse -> via neutrino interaction one of the protons transmutes to a neutron to form deuterium -> combines with another proton to form a helium nuclei -> two helium nuclei fuse releasing alpha particles and two protons). The weak force is also necessary for the formation of the elements above iron. Due to the curve of binding energy (iron has the most tightly bound nucleus), nuclear forces within a star cannot form any element above iron in the periodic table. So it is believed that all higher elements were formed in the vast energies of supernovae. In this explosion large fluxes of energetic neutrons are produced which produce the heavier elements by nuclei bombardment. This process could not take place without neutrino involvement and the weak force.
Electromagnetism:
The electromagnetic force is the forces between charges (Coulomb’ Law) and the magnetic force which both are describe within the Lorentz Force Law. Electric and magnetic forces are manifestations of the exchange of photons. A photon is a quantum particle of light (electromagnetic radiation). This particle has a zero rest mass, however, light has relativistic mass (since its traveling at the speed of light “C”) and can be acted on by gravity. The speed of light in a vacuum is a constant and is unobtainable by matter due to the lorentz transformation. Electromagnetism obeys the “inverse square law”.
Gravity:
Gravity is the weakest of the forces and also obeys the inverse square law. The force is only attractive and is a force between any two masses. Gravity is what holds and forms the large scale structures of the universe such as galaxies.
You neglected to mention the mysterious "ID force," which -- although unobserved and unexplained -- rules the process of evolution.
</creationism mode>
Up, charm, and top use the gluon for their force carrier.
Down, strange, and bottom use the photon for their force carrier.
All six quarks are acted upon by gluons and photons. This is because all of them carry electromagnetic charge (u,c,t have a charge of +2/3 e, while d,s,b have a charge of -1/3 e), and all of them carry a color charge. There are three kinds of color charge, which are commonly written as red, green and blue. Every quark in the universe has one of these charges. Each flavor of quark can have any color charge.
(Geek alert: because there is one kind of EM charge, there is one photon, but since there are three kinds of color charge, there are eight gluons. Gluons themselves carry both a color charge and an anti-color charge, so you'd think that there would be nine gluons, but the combination red-antired + blue-antiblue + green-antigreen is colorless, so if you define a red-antired gluon and a blue-antiblue gluon, a green-antigreen gluon can be described as a superposition of the other two. Only eight gluons are needed to span the color space.)
E neutrino, u neutrino, and t neutrino use the W boson for their force carrier.
Electron, muon, and tau use the Z boson for their force carrier.
All quarks and leptons couple to both W and Z bosons. A W, for example, transforms an electron to an electron neutrino, or a t-quark to a b-quark.
Strong – The pion (and others)
Not wrong, exactly. The pion does mediate the inter-nucleon force. That force isn't fundamental, however. The fundamental force is the inter-quark force that binds the quarks into hadrons (such as protons, neutrons and pions), and that is what we usually mean by the strong force, nowadays. The force between hadrons is a residual color dipole interaction that is analogous to the Van der Waals force in electromagnetism.
The weak force is also necessary for the formation of the elements above iron. Due to the curve of binding energy (iron has the most tightly bound nucleus),
The curve of binding energy comes from the strong and electromagnetic forces. The role played by the weak interaction is to convert protons to neutrons and vice-versa, which is often required to make stable nuclei out of two lighter ones.
This particle has a zero rest mass, however, light has relativistic mass (since its traveling at the speed of light “C”) and can be acted on by gravity.
The relativistic mass of a photon is also zero. Gravity couples to energy density, which is typically dominated by mass. But even in Newtonian gravity, massless light particles will bend in a gravitational field (the trajectory of a test particle doesn't depend on mass).