Strasser and the other left wing "National Bolsheviks" like Goebels likely take over the party. Goering and the other right wing members probably leave at some point and either form a new party or join an existing one like the DNVP.
Since the Nazis were a minor, and rather ineffectual protest party prior to the Great Depression, we won't see any real divergences in German politics until the 1930 elections.
The real question is how will the national conservative vote go? Will the DNVP be able to consolidate it amongst themselves? Do they cooperate with another nationalist group lead by Goering and other populists in a united front? Do they simply split the vote?
The German Communists do not have a chance of winning any election. They have a limit in terms of how popular they can get, and none of the other major parties would ever form a government with them. At best, they top out at 15%-20% or so. More likely, they top out at 10-15%, with the Strasserite Nazis splitting the vote of the radical workers.
Hitler had an extreme self assurance that he could become Chancellor on his own and refused to join any coaltion he could not dominate. I don't see any other right wing leader doing that. Most likely, a revived DNVP/conservative alliance might take power, but only in cooperation with the Hindenburg camarilla, and not with the power Hitler took in 1933. Instead, we might see a Goering/Hugenberg/Papen coalition form with no single party dominating things (IOTL the Nazis did not initially dominate either, but Hitler was very shrewd and lucky and was able to consolidate power very rapidly). Another possibility is that the democratic parties - the SPD, Centre and perhaps one of the liberal parties - are able to regain control of the Reichstag.
In any case, the Reichstag is likely to be fractious. The real decision point is what happens when Hindenburg dies in 1934. I don't see anyone able to assume Hindenburg's powers like Hitler did, so there will be another election. Either a national conservative or the SPD will likely be elected president, but I'm assuming one of the conservatives will likely grab it.
As the worst of the Depression ends and things improve, politics will begin to become normal again. There will still be political violence and instability, but no dictatorship. Germany will seek to overturn Versailles, but not by war.
The beginning of the Spanish Civil War might radicalize things a bit, but I think German democracy - as it were - will survive. Without a Nazi Germany to counterbalance, we might see Britain and France take a much harsher stance against Italy when it attacks Ethiopia. If so, there could be all sorts of butterflies as the League of Nations isn't see to be weak. If so, there might even be a political solution to the Marco Polo Bridge Incident (although I think the most likely course here is the Sino-Japanese War as normal).