If the currants are hard, cover them with warm water and set them aside to soften while you cut the celery and apples. When they're soft, after 10 minutes or so, drain them and squeeze out the water.
Separate the stalks of celery and peel the tougher outer stalks. Slice the celery into thin pieces, straight across or at an angle. Cut the apples into quarters or sixths if they're large and thinly slice them crosswise. Finely chop the celery leaves and the parsley and crack the nuts.
Combine the celery, apples, currants, celery leaves, parsley and walnuts in a bowl. Toss them with just enough walnut oil to coat everything lightly. Add the lemon juice or vinegar to taste, salt lightly, season with pepper and toss again.