Pandas left outer join multiple dataframes on multiple columns

Merge them in two steps, df1 and df2 first, and then the result of that to df3.

In [33]: s1 = pd.merge(df1, df2, how='left', on=['Year', 'Week', 'Colour'])

I dropped year from df3 since you don't need it for the last join.

In [39]: df = pd.merge(s1, df3[['Week', 'Colour', 'Val3']],
                       how='left', on=['Week', 'Colour'])

In [40]: df
Out[40]: 
   Year Week Colour  Val1  Val2 Val3
0  2014    A    Red    50   NaN  NaN
1  2014    B    Red    60   NaN   60
2  2014    B  Black    70   100   10
3  2014    C    Red    10    20  NaN
4  2014    D  Green    20   NaN   20

[5 rows x 6 columns]

One can also do this with a compact version of @TomAugspurger's answer, like so:

df = df1.merge(df2, how='left', on=['Year', 'Week', 'Colour']).merge(df3[['Week', 'Colour', 'Val3']], how='left', on=['Week', 'Colour'])