First up: Honor tiles. Here are the scoring patterns for this category:
3.0 Honor Tiles
3.1 Value Honor : 10 per set
3.2.1 Small Three Dragons : 40
3.2.2 Big Three Dragons : 130
3.3.1 Small Three Winds : 30
3.3.2 Big Three Winds : 120
3.3.3 Small Four Winds : 320
3.3.4 Big Four Winds : 400
3.4 All Honors : 320
The advantage of building a hand with the rare honor tiles is the potentially very large scores. The disadvantages are many, too. First, you need to be pretty lucky to even complete sets of honor tiles since they are so rare. Second, you need to be extremely lucky to get the tiles yourself, or you need to call discards and expose your hand, and everyone will be able to see what you're up to. Third, honor tiles are often discarded early in the game, before you're ready to claim them. Fourth, again because of the scarcity, the patterns take a long time to complete.
All in all, honor patterns score well because they are rare and hard to build, but they are the easiest to understand. Honor tiles are also usually very safe to throw near the end of the game if one has been seen. Keep in mind they can be used to complete a pair, and that someone with a concealed hand could be going for Thirteen Terminals and might need your single honor, even if three of them are out.
3.1 Value Honor
A value honor set is a triplet (or pung) of any dragon or of your seat wind, meaning East if you are the dealer and so on. This is the only pattern you can score multiple times in your hand. Potentially, you could score it four times.
Statistically, this pattern is slightly over-valued. This honors the tradition from Chinese Classical and emphasizes these tiles, encouraging players to hang on to single, valued honor tiles until someone else discards one. People sometimes will keep such a tile until two are discarded, or even keep it as the last one to discard when they become ready, as a safe discard.
3.2.1 Small Three Dragons
This pattern means that you have triplets of two dragons, and a pair of the third. Getting that third set completed is tough, but you're most of the way there. This pattern scores 40 points itself, but don't forget you've got two dragon pungs, and those score another 10 points each, so you should always score at least 60 when you have this. You can often add Four Triplets or Outside Hand (Terminal or Honor in Each Set). If you also have two wind triplets, suddenly you've got All Honors and have reached the listed limit of 320 points!
3.2.2 Big Three Dragons
One triplet of each of the three dragons. Also score each of those as a value honor, so you have at least 160 points.
3.3.1 Small Three Winds
Triplets of any two winds, plus a pair of a third. Add in Value Honor if one of the triplets is your seat wind.
3.3.2 Big Three Winds
Triplets of any three winds. Add in Value Honor if one of the triplets is your seat wind.
3.3.3 Small Four Winds
Triplets of any three winds, plus a pair of the fourth. This is a listed limit hand, so you can only score one pattern - you cannot add Value Honor or any other pattern with a pattern this big.
3.3.4 Big Four Winds
Triplets of all four winds. Again, this is a listed limit hand, meaning you cannot score any other patterns with this one.
3.4 All Honors
All your tiles are honor tiles. You could do this with something like two dragon triplets and three small winds (also four triplets), which would otherwise score 10+10+30+30 or 80 points. You could also do it with seven pairs of honors, which would otherwise score you a measly 30 points. This is an impressive and beautiful hand when you can do it. It is a listed limit hand, so you cannot add any other patterns. Be happy with your 320 points!