Ranking order of nucleophilicity
The first thing to note is that nucleophilicity is a kinetic parameter that cannot be addressed easily with thermodynamic parameters such as electronegativity. Instead, you need to inspect all potential nucleophiles by their kinetic merits.

One easy thing that we can use, even though it is thermodynamic, is the effective charge. The centre of negative charge of the acetate molecule is somewhere in the middle between the two oxygens and that of tosylate is somewhere in the middle between three equivalent oxygens. Also, in both systems the oxygens are bound to very highly oxidised atoms ($\ce{C^{III}}$ and $\ce{S^{IV}}$, respectively), which greatly reduces their electron density and thus their desire to attack nucleophilicly. Finally, in acetate’s case the nucleophilic attack would reduce the effectiveness of the carboxylate resonance as one of the two mesomeric structures becomes disfavoured (charge separation) which adds another grain of salt against nucleophilic attacks.

Tosylate is less nucleophilic than acetate because there are three oxygens than two but they only bear a single negative charge between them.

Now onto cyanide and methanolate. For cyanide, first note that it is both $\ce{C}$-nucleophilic and $\ce{N}$-nucleophilic. Since the HOMO, the highest occupied molecular orbital, has a much larger contribution on the carbon side, the $\ce{C}$-attack is strongly favoured over $\ce{N}$-attack and we can ignore the latter.

We can again use the bond-partners argument here. The oxygen of methanolate is bonded to a $\ce{CH3}$ group which, in general, is electron donating, thus increasing its electron density. The cyanide carbon, however, is bonded to the more electronegative nitrogen which slightly reduces its electron density. Thus, we can infer that methanolate should be a better nucleophile than cyanide. (Note, however, that both are very good nucleophiles, especially when compared to the other two.)