An anti-particle is the partner of a particle but with all its properties, except its mass, inverted. For example, the anti-particle associated to the electron is the positron whose electric charge (+1) is the opposite of the charge of the electron (-1). When a particle meets its anti-particle they annihilate and their mass is converted into energy. This happens, for example in leptonic colliders where an electron and a positron annihilate and release all their energy...
Atoms are "the building blocks" used to construct the different materials we know. The atoms often gather in groups called molecules. The atoms are made of a an nucleus surrounded by a cloud of quarks.
A collider is a big device (typically a few km long) that accelerates particles and smashes them on each other (they collide). Usually a collider is made of 2 particles accelerator that accelerate particles in opposite directions before collinding them.
A hadron is a particle made of 3 quarks. The proton and the neutron are examples of hadrons.
Leptons are fundamental particles. The best known lepton is the electron. The other known leptons are the muons, the tau and the neutrinos associated to the electron, the muon and the tau.
There is no "exact" definition of a particle. Here it can be considered as any of the "brick" that can be used to build an atom. This definition includes the proton, the neutron, the electron, the quarks... The "particles" used in particle physics are not related to the "particles" used in chemistry.
A quark is a particle with an electric charge of 1/3 or 2/3. Protons and neutrons are made of 3 quarks.
The Standard model is the theory describing the interactions between the fundamental particles. More etails on the standard model can be found here.
Supersymetry, alos known as SUSY is a theory that extends the model standard by giving a "superpartner" to each of the known particle. It is one of the candidate theory beyond the standard model.