function AnsiInspect(S,look_for,replace_with : string) : string;
var i : Integer;
    D : AnsiString;
begin
  D:='';
  while Length(S)>0 do begin
    i:=Pos(look_for,S);
    if i=0 then begin
      D := D + S; S:='';
    end else begin
      D := D + Copy(S,1,i-1) + replace_with;
      Delete(S,1,i-1 + Length(look_for));
    end;
  end;
  Result := D;
end;

var InpStr,OutStr : string;
begin
  ..... // InpStr füllen
  OutStr:=AnsiInspect(InpStr,'ö','oe');
  OutStr:=AnsiInspect(OutStr,'Ö','Oe');
  OutStr:=AnsiInspect(OutStr,'ä','ae');
  OutStr:=AnsiInspect(OutStr,'Ä','Ae');
.....

end.