#C, 138 135 bytes
char*s="aiueokstnhmyrw";i,j;k(*v){j=strchr(s,*v>>8)-s;i=strchr(s,*v)-s;j=i<4?i++:j<4?j-~(2520%i&3):!++i;printf("%c%c",s[i],i<5?:s[j]);}
13 of 14
deleted 3 characters in body
user56344