The past tense marker is -li-, and is used in a main clause verb. The other two are dependent forms, and are not restricted to the past: -ki- is simultaneous and -ka- is consecutive. A simultaneous action could often be translated with the English -ing form:
nalimsikia akisema . . . = I heard him saying . . . (= when/while he said)
Consecutive actions are often used in past narrative, starting with the -li- tense, then each -ka- form corresponding to "and":
alikwenda mjini akasema . . . = he went to the village and said . . .
(cf. alikwenda akisema = he went saying)