Solutions :

3-letter words (1 point): 31

CEE; EEN; ENE; GEE; GEM; GEN; GEO; GHI; HEM; HEN; HIE; HIN; HOE; INN; IRE; JEE; MEE; MEG; MEN; NEE; NEG; NIE; REE; REI; REN; RHO; RIN; RIZ; ZEE; ZHO; ZIN.

4-letter words (1 point): 16

EINE; GEEZ; GENE; GHEE; HEIR; HIRE; JEER; MEIN; MENE; NENE; REEN; REIN; RIEM; RINE; ZINC; ZINE.

5-letter words (2 points): 6

EERIE; GENIE; GENII; HIREE; RENNE; RHINE.

6-letter words (3 points): 6

HEEZIE; HENNER; MENEER; MENHIR; NEINEI; RENEGE.

7-letter word (7 points): 1

HENNIER.