Strategies

Cultivate and protect your province before attacking.  The more you develop your province, the more stuff you'll have at your disposal when it comes time to amass that big army.  Protection also seems to help a bit when it comes to keeping enemy troops out of your province.  If you get lucky (which you most likely will), if you keep to this policy you'll end up with a Pastha for your troubles, which is better than a fickle bunch of mercenaries any day.
 
That brings me to fifth units.  There are a few which are excellent to hire, but most of them will either desert you or just end up being worthless.  If you can, grab yourself a Wyvern, as they can stand up to most units and sustain little damage, and they kick serious ass on the offense.  All that, and they fly too!  I have developed new respect for the Fachan, since it's counted as a long-ranger and can attack anything within two spaces.  Spearmen are good to have because they're cheap, come in large quantities, and will aid even a lower-level family.  You might want to try out the Gunners a couple times just because they have cannons, but they're not as strong as they look.  Warriors are greately overestimated, in my experience, since by the time your fame is high enough that they won't just desert automatically, you should already have multiple gems.  Just do some development and wait for a Pastha.

Armies:  if at all possible, don't recruit too many soldiers at a time.  The fates will curse you if you do.  Try to recruit only when your advisor tells you to, or when you already have high levels of cultivation, protection, and loyalty.  Only recruit a lot at a time if it's absolutely necessary (as in it's the only thing standing in the way of you getting your province taken away from you).

You may be wondering about loyalty.  What does it do, anyway?  Well, in addition to keeping your army from deserting you, it increases your cultivation at least as much as cultivating itself.  (For instance, if you're at zero loyalty, you're not going to get any food that harvest, no matter how much cultivating you've done!)  If at all possible, get your loyalty close to 100 before September of every year.

Searching does more than just check out which silly fifth units other people have - it can also get you some cool items.

Every character's attributes increase variably every year until he or she turns 65.  At this point, the character will get -5 from each attribute until he or she dies.  All characters die at age 75; however, if more than one character reaches 75 in the same year, they will sometimes die in different months.  The death can be delayed by resetting the game after the character dies, but keep in mind you're going to have to do this every month in order to prevent the death entirely.  (I once lost a game when Erik turned 75 and Elias, his only heir, had been banished a few months earlier.  Oops.)

Do your cultivation February-August, and protection September-January.  This way, you'll get the maximum possible cultivation for the September harvest, and have high protection in the winter.  The best way to handle loyalty is to give 100 food in August - that oughta shut them up.

That is, unless you're Pender (or someone else with horrific charm), because not only does charm make it more likely that someone will join you, it also affects how much your loyalty increases every time you give food.

Here's an important cheat to keep in mind if you want to make the game even easier:  You can avoid plagues, storms, earthquakes, and other bad events simply by reloading the game afterwards.  Technically speaking, you can keep doing this until the provinces you want get hit with the event, but it can take a while.  (Though if you're looking to invade someone, they'll lose 20% of their army if they get plagued!)

Never underestimate the power of sabotage.  Everyone always goes for plundering, since you get free stuff, but sabotaging is where the real power is, especially in early scenarios where your main adversary is Lankshire.  When you successfully sabotage a province, it decreases cultivation, production and army strength.  Therefore, if you're up against a province with a large army, a turn or two of sabotage will lower their strength enough that you'll be able to defeat them with ease.  Note that sabotage seems to work far better against Lankshire than any other family.

You can banish Eselred by isolating his home province first, but why would you want to?  All of his heirs are stronger than he is!

Keep basic economics in mind when trading:  buy when prices are low, sell when prices are high.  Avoid doing either when prices are average unless it's absolutely necessary.  Not a difficult concept in my opinion, but if it were that easy they wouldn't have to have economics classes, now would they?

In a manor, the ruler's attributes decrease by 50%.  Therefore, even if all your vassals are losers, you may be better off giving them provinces rather than letting the prince or princess handle it all.

To move your home province, select "Change Lord" and choose the new province.  When it asks "You, Lord, or Vassal" go to "Lord" and choose your current home province.  "OK to move yourself?" will come up, and when you select yes, the provinces will be switched.  This action may only be performed once per turn, so if you mess up you'll just have to reset.