Dinner Plates

Clue1:
 The object is to create five stacks of two plates on every point of the star pattern.
Clue2:
 A plate must jump two plates, stacked or not.
Clue3:
 Once moved, a plate cannot be moved again.

Solution:

The object of this is to get a stack of two plates at each point of the star.  To do this number the plate at the top #1.  Then number the others 2-10 by going clockwise.  Thus 1,3,5,7,9 should be at the points of the star.  Then make the following moves:
6 to 3.
8 to 1.
4 to 9.
10 to 7.
2 to 5.

There are other solutions, but one is enough.

Doll House

Clue1:
 Get five of your pieces in a row, or capture five pairs of your  opponent's pieces to win.
Clue2:
 Try not to let Stauf get four unchecked pieces in a row or else you are doomed.

Solution:

Try this:
First three moves put your stones under Stauf's
Fourth move, block Stauf to the right of his three stones
Fifth move, fill in the middle of  your two stones
Sixth move, fill in four in a row by going right Stauf will take two of your stones
Seventh move, fill in your row again

YA GOT HIM!

This seems to always work when Stauf's second stone is to the right, but it can work when he goes left also
 
Another Note: this does not always work, but it is a good starting point to see what Stauf does.

FAUST Train

Clue1:
 Manipulate the cars by switching between the top and the bottom track. Use the switcher.
Clue2:
 The letters will spell out "STAUF".

Solution:

First of all, I'll be calling the track that goes straight through, the main track. I'll be calling the track that curves around, the side track. I'll call the section where the AUST starts to be the end section.  The goal of the puzzle is to rearrange the letters to get STAUF in the end section.  The puzzle starts with F on the main
track and AUST on the end section.

First: Move the AUST one at a time to the main track so that we get TSUAF on the main track.

Second: Move the TSUA to the side track so that we get AUST on the side track.

Third: Push the F into the end position.

Fourth: Push the A into the end position.

Fifth: Move the UST to the main track to give us TSU on the main track and AF in the
end section.

Sixth: Move the A onto the main track to give us ATSU.

Seventh: Move the ATS to the side track giving us STA there.

Eighth: Move the U into the end position.

Ninth: Move the STA to the main track giving us ATS.

Tenth: Move the ATS one at a time into the end section giving us STAUF there.

So the moves should look like this:

Beginning:
      F   AUST
After First:
   TSUAF
After Second:
       F
    AUST
After Third:
              F
    AUST
After Fourth:
             AF
     UST
After fifth:
     TSU     AF
After sixth:
    ATSU      F
After seventh:
       U      F
     STA
After eighth:
             UF
     STA
After ninth:
     ATS     UF
After tenth:
          STAUF

Furniture

Clue1:
 Move the pieces around until you can move the piano off the board.
Clue2:
 This one's difficult.

Solution:

I got this third hand, so I don't know who originally did this.  Anybody?  Bueller?

Also, there may be some typos in the solution.
Number couches 1-4
1 being lower left
2 being upper left
3 being lower right
4 being upper right
Letter Chairs A,B,C,D from bottom to top.
Letter Table T  and the Piano P

T, R means move table to the right
B, R
A, U,R means mve chair A up then right
3, L
T, D
B, R

A, U 3, U 1, RX2 P, D C, LX2 A, LX2 B, LX2 4, D D, RX2 2, RX2 A&C U P, U 1, LX2 3, D B, D,R P, R C, D A, L,D 2, LX2 D, LX2 4, U B, U,R P, R C, R,U 1, U 3, L P, D D, D,R 4, L B, U D, R P, U 3, RX2 1, D A&C, D 2, D 4, LX2 P, U A&C, RX2 1, U 3, L C, D,L T, L D&B, DX2 P, R A&C, UX2 T, L B, L,D P, D,R

Hexagon

Clue1:
 To win, be the first to create an unbroken path that touches all three sides of the triangular field.
Clue2:
 A corner hexagon counts as touching two sides at once.

Solution:

Try filling one of the sides.  I won the first time through by filling the bottom row.  But, you can't just start at one end and go straight across.  Try to fool Stauf by placing them in at random and even put some pieces around elsewhere on the board.

Jewel Box - Gems

Clue1:
 Each gem must be adjacent to a gem of a matching color.
Clue2:
 You can rotate a cluster of gems or swap positions with another cluster.

Solution:

Label the gems 1-6, going clockwise, with 1 being at the top.
1. Switch gems 1 and 2.
2. Rotate gem 4 to get red or blue as the top color.
3. Rotate the rest of the gems starting at gem 5, matching the adjacent color of gem 5 to gem 4, then move on to gem 6, then 1, 2, and 3, matching the adjacent colors.

That's it.  I am sure that there are more solutions, but that was the first one I did.

Modern Art

Clue1:
 The selected section gets colored in as well as all adjacent to the selected section.
Clue2:
 You're playing against Stauff.  His moves are grey.
Clue3:
 The goal is to fill in the last square.

Solution:

Make your starting move at the blue L in the lower middle of the painting. Then it should all be downhill from there.

Mouse Maze

Clue1:
 Build a path for the mouse.
Clue2:
 Placing a maze piece causes the other pieces in the row to slide over or in a column to slide up and down.
Clue3:
 After a piece is played, you may move the mouse to any location along the newly created path.

Solution:

Ok, all I can do is suggest a few strategies. First, always move the mouse as far away from Stauf's hole as possible.

Second, work on building multiple path options to your hole, or multiple possibilities.  Don't concentrate on one sure path.

Third, sometimes Stauf will work with you, well, Stauf doesn't realize this, but when I played he made two moves that destroyed my original plan, but opened up a door for me to win in one move. ;)