
Ouachitonian |

Assume a custom Paladin archetype that grants Spellstrike. Which spells should I use with it? I guess Cure spells work when fighting undead, but…I’m not seeing much else on the normal list. What am I missing?
I know the Unsanctioned Knowledge feat, which will at least get me access to Inflict spells, but I’m sure there are better options I don’t know of because I don’t often play bad touch clerics/oracles/inquisitors.
Are there other ways to get other spells on my class list? Something like a Ring of Spell Knowledge, but for prepared divine casters?

Azothath |
since Paladins don't get a lot of spells and it only applies to touch spells, I'd say "None". You'll probably spend/lose too many class abilities to get Spellstrike than it is worth. You're not a cleric, wizard, or magus.
You are fighting weaponwand:T1, reach metamagic.
Spelllcasting: the easiest is just dip into diviner wizard 1. It costs a level but does an end run around UMD for all the good arcane spells. Paladins are MAD so it is not a big deal. The other is Cleric varisian priest it's just not as good spell list.
Pearls of power. Maybe leave a slot open.
Just get wands for First SplLvl useful & defensive spells. Scrolls for stuff you don't use very often.
There are some items but it can turn into a resource(cash) drain.

Mysterious Stranger |

The only paladin spell that would be worth using with spell strike would be dispel evil or dispel chaos. Anything else including cure spells are not worth using. The paladin is simply not an offensive caster so does not have any spells that work well with spell strike. Most of their most effective combat spells are those that increase their combat. Why bother casting cure light wounds to deal an extra 1d8 +5 points of damage to undead when you could cast bless weapon or divine power.
You might not find play something else to be useful advice, but it is true. Any paladin ability you traded for this was more powerful than this unless it gave you access to some decent attack spells at the same time.
Spell strike may also cause the paladin to provoke an AoO when casting his spell. Since the paladin will probably be prioritizing STR over CHA and takes a -3 penalty to caster level he will have a hard time making the concentration roll to cast defensively.
Spell combat could be useful for a paladin as it would allow him to cast a buff spell while getting a full attack. But Spell Stike is likely to do more harm than good.

DeathlessOne |

... Yeah, there are not very many spells (barely any at all) for a Paladin to make use of with Spellstrike, aside from Cure Wounds spells. Trial by Fire is one, but you really want spells that deal just damage and not rely on saving throws, but those that allow for saving throws give a level of control of the battlefield or debuff.
You definitely want Unsanctioned Knowledge. Spells of interest to you would be:
1st level Bard: Touch of Blindness and Touch of Gracelessness
2nd level Bard: Shadow Anchor and Touch of Mercy
3rd level Bard: Flexible Curse, Isolate, and Jester's Jaunt
4th Level Bard: Alaznist's Jinx, Aroden's Spellsword*****, and Kiss of the First World
1st Level Cleric/Oracle: Touch of Blindness and Touch of Bloodletting
2nd level Cleric/Oracle: Disfiguring Touch, Suns's Disdain and Touch of Mercy
3rd level Cleric/Oracle: Bestow Curse, Fair is Foul, Forced Mutation, Irregular Size, Sands of Time, Sebaceous Twin, Steal Years, Trial by Fire, Trial of Fire and Acid,
4th level Cleric/Oracle: Black Spot, Cure of Unexpected Death, Poison and Spell Immunity
1st Level Inquisitor: Touch of Combustion
2nd Level Inquisitor: Brand of Hobbling, Stricken Heart, and Sun's Disdain
3rd Level Inquisitor: Banish Seeming, Cast Out, Flexible Curse, Forced Mutation, Isolate and Trial by Fire
4th Level Inquisitor: Brand of Tracking and Greater Brand
As you can see, the Cleric/Oracle list have the most abundant spells to pick from. I'd personally grab spells from the Bard list as Aroden's Spellsword is incredibly useful overall but thats a long term investment. All the 'curse-like' spells from the Cleric/Oracle list are all fun and flavorful but might not be something a Paladin would dabble in.
Are there other ways to get other spells on my class list? Something like a Ring of Spell Knowledge, but for prepared divine casters?
Samsaran as a race choice plus their alternate trait "Mystic Past Life" would allow you to select from another spell casting class (has to be divine as you are a divine caster). Might be a way to get the bard spells you want with Unsanctioned Knowledge and some of the fun spells from the Cleric/Oracle list.

Phoebus Alexandros |

OP, I'm surprised that your GM is making a paladin archetype that has spellstrike as a key class feature... but not an expanded spell list to make use of it.
The other thing that I'm curious about, but which is maybe neither here nor there, is whether this archetype also has a means to incorporate its spellstrike into a full attack, a vital strike, a charge, etc.