When I encounter a puzzle that results in all X's and no positive clues, I usually do the following steps:
1. Check for intersections as described in this thread's first reply. I look for category blocks that have a lot of X's - especially ones that have a lot of rows or columns with only two remaining openings. If you find two rows or columns that, when combined, have an X in every cell, you know that combination can never be true.
2. Check for columns in the category blocks in the top row that are related by an order
clue stating that one element is a fixed distance
from the other. A typical example would be something like: "Jason arrived one day
later than Megan." If only two days remain open in each column, then you can X out the overlapping day in the other columns
Example: If Jason can only be Tuesday and Wednesday, and Megan can only be Monday and Tuesday, then either Jason or Megan has to be Tuesday. Therefore, no other person can be Tuesday.
3. Check for situations where two members of a category have only two choices left, and those choices are the same
for both members.
Example: Both Kaitlin and Nehemiah can only be Monday and Tuesday. All the other days for both of these names are X'd out. This means that either Kaitlin is Monday and Nehemiah is Tuesday, or Kaitlin is Tuesday and Nehemiah is Monday. Either way, no other name can be associated with Monday or Tuesday. Usually when I find one of these, I can place a lot of Xs.
4. Go back and get some more information from the ordering clues and the "Of Noah and the person who arrived on Monday, one likes shopping, and the other lives east of city hall."
Using this "Of Noah ..." clue as a concrete example:
a. Determine which days of the week are possible for Noah. We already know that Noah cannot be Monday from the clue. If only Tuesday and Wednesday are the only remaining possibilities for Noah, then for the proposition to be true, shopping and east of city hall can only be Monday, Tuesday, or Wednesday.
In practice, I look for X's in Noah's row or column that are in addition to Monday, and then I add the corresponding X's to shopping and east.
b., c., d. Do that for each of the four parts of the "Of Noah ..." clue. You will usually get several X's. I.e. (b.) determine which first names are possible for Monday, (c.) determine which locations are possible for shopping, and (d.) determine which hobbies are possible for east of city hall.
There is probably a pattern match technique for doing this logic, but I haven't progressed this far yet. Still a beginner.
e. Do the same sort of thing for the ordering clues. You might find a relationship such as:
B1 or B2 arrived later than B2 or B3. Where B is a particular category.
Normally the above situation would have 4 possible combinations. B1 later than B2, B1 later than B3, etc.
However, since B2 cannot be later than itself, this can result in another X.
5. Remember to place an X for the "Either the person who arrived on Tuesday or the clarinet player ..." or "Neither the person who arrived on Tuesday nor the clarinet player ..." clues. The two category members mentioned are not the same person. This is obvious when the two members are in the same category, but it's not so obvious when they are in different categories.
6. If all of the above still doesn't lead to the solution, then look in each category block for situations where a category member only has a couple choices left. Look in the grid to see what would happen if each choice was taken. Sometimes, the constraints in the other category blocks will exclude all the choices in a particular category. This is a variation of #1 above where a combination results in Xs in every cell.
Example: Categories are Weekday, First Name, Holiday, and Gum. If you get to the point where the remaining choices for Adam are Juicy Fruit or Dentine, and picking Juicy Fruit would exclude Adam from any of the holidays (because of existing constraints in the grid), then Adam cannot be Juicy Fruit. Adam has to be associated with one element in each of the categories, and in this example, Adam has to be associated with a holiday.
7. Finally, if after doing all of the above the puzzle still cannot be solved without a guess of some sort, in my case, it is usually because I've missed an X or I've placed an X in the wrong place. I usually have to push the reset button and try again.