Poirot - IXTJ - not sure whether he's S or N because on the one hand he's extremely traditional and has enormous respect for social norms and historical ways of doing things and he's very conservative (Si), but on the other hand he uses introverted intuition to form gut instincts about what is going to happen in the future and work out who is lying to him and discover hidden motives (Ni). He's also very arrogant and always thinks he's right, which can be typical of either type. The very high value he places on intelligence and the high standards he sets for himself (and others), though, suggests INTJ.
Hastings - ESFP - he's got an adventurous spirit, he's very gullible and not very good using 'his little grey cells', and he also likes to have fun.
Ariadne Oliver - ENFP - she's very intuitive, abstract, and absent minded/all-over-the-place, her creativity suggests F, although she comes across as more of a thinker (ENFPs use Te as their tertiary function)
The other characters I have no idea about - sorry
