How are neutral amines effective bases in organic chemistry?
There are several interesting aspects to your question.


  How are neutral amines effective bases in organic chemistry?


First of all, recall the definition of a base. Anything which accepts a proton (or donates a pair of electrons) is a base. Organic bases are very strong and corrosive! These bases should not be undermined, even though they may sound weak (and their stench is worse than inorganic bases). Your lye-free oven cleaner has an organic base, an neutral organic amine such as ethanolamine, which dissolves dirty grease stuck in the oven. This molecule has no charge yet it is a strong base, acting just like sodium hydroxide based oven cleaner in terms of performance.


  Thus, hydroxides and alkoxides are superior alternatives to these
  amines.


The second reason to avoid hydroxides and alkoxides is their solubility in organic solvents. Neutal organic amines easily dissolve in toluene and a variety of organic solvents. NaOH or NaH remain as a suspension.


  MOMCl  uses large bulky amines to deprotonate the alcohols, rather
  than using hydroxides


Again you have to think about the reaction solvent. Is an inorganic hydroxide soluble in your solvent? Then comes an important point. Why use bulky amines? Their sole purpose is to act as a proton sponge in the reaction mixture and prevent the formation of free acid. Bulky amines are preferred so that they don't react easily with the alkyl chlorides or acyl chlorides, thus prevent the formation of their own undesired side products.