Grums was an annex in a set of parishes sometimes called a deanery ("Pastorat" in Swedish). There are no less than five parishes in the same deanery, all of which would merit further investigation for likely candidates. The parishes are Nor, Grums, Ed, Segerstad, and Borgvik. The principal parish was Nor, but it could easily be that Anders was born in any of the other associated parishes.
Searching through some of the volumes of births for these parishes yields the following candidates (note there may be further volumes to check - I've only done the obvious ones):
Anders - born 19 Oct 1834 in Nor parish, son of Jönas Andersson (an unusual spelling - it could be either Jonas or Jöns or the rather exceptional Jönas... There *does* appear to be an umlaut over the o...) and his wife Britta Nilsdotter at Mellemstorp (?), see: Nor (S) C:2 (1823-1860) image 35 (reference to AD image, may be different at Riksarkivet).
Anders Gustav - born 28 March 1834 in Eds parish, son of Johannes Andersson and Kjerstin Olsdotter at Ås, see Ed (S) C:4 (1820-1858) page 95
Anders - born 27 November 1834 in Segerstad parish, illegitimate son of the maid Maja Pettersdotter, see Segerstad (S) C:2 (1794-1861) page 183
Borgvik yielded no candidates.
If I were you, I would follow up on the above candidates to see if their continued existence would overlap with your Anders Jönsson. I would also go through the volumes of births and christenings in more detail - I've only skimmed them here, and could easily have missed something.
Do let us know how you go! :)