How can K (kaon) and Σ (sigma particle) be created quickly via the strong interaction and decay slowly via the weak interaction?

Kaons and sigmas contain strange quarks, so the "ground state" particles must decay by changing quark flavour. The strong and electromagnetic interactions cannot change flavour, but the weak interaction can, hence they can only decay weakly.

The strong interaction can easily produce $s\overline{s}$ pairs, which can subsequently pair up with lighter quarks to produce strange hadrons (including kaons and sigmas) without the need for any flavour-changing processes.

What one has to keep in mind: that the strong interaction is called strong because it is terribly binding. Quarks interact with all three, strong, weak and electromagnetic, and a strong interaction can produce quark antiquark pairs, conserving all quantum numbers, thus the strange mesons ( and baryons) will be coming in pairs, one having grabbed an s quark and another an anti-s quark. Once paired into a meson or baryon the quarks are stable, and if there were no weak interaction , they would never decay. It is the weak interaction that allows for the decay, makes accessible the lower mass energy states of the decay channels.