A soliton is a localized, non-dispersive solution of a nonlinear theory in Euclidean space. It certainly is a real object: you have a famous story about a certain John Russell who observed soliton-like waves made by a boat on a river (wikipedia knows everything about it!)
The so-called morning glory clouds in Australia (http://en.wikipedia.org/wiki/Morning_Glory_cloud) are also a great example.
The theoretical physicist Sidney Coleman uses also the term 'lumps' to denote solitons, his book 'Aspects of Symmetry' contains a great chapter on them (and another chapter on instantons, for that matter). The terms 'kinks' and 'anti-kinks' are used for the soliton solutions of the sine-Gordon equation, I do not know whether these terms are used outside that context.
Instantons (the term coined by 't Hooft , who did groundbreaking research on them), or pseudo-particles (the name given by Polyakov ), are not real, in this sense that they are solutions to the equations of motion of a quantum (field) theory after a Wick rotation, in which time is made imaginary! Therefore, they are not observable as such, but they can be used to calculate and to explain quantum mechanical effects that can be observed, such as tunneling. In QCD, instantons are believed to tunnel between the topologically different color vacua, although I have to admit I don't know the details.
Good sources on these matters are:
 't Hooft, Phys. Rev. D14 (1976) 3432
 Polyakov, Nucl. Phys. B120 (1977) 429
Coleman - Aspects of Symmetry - Cambridge University Press (1985)
Vainshtein, Zakharov, Novikov, and Shifman - Abc of Instantons - Sov. Phys. Usp., 25:195 – 215 (1982)
Schulman - Techniques and Applications of Path Integration - John Wiley & Sons