  (Abridged) We present high spatial resolution ultraviolet and optical
spectroscopy, obtained using the Space Telescope Imaging Spectrograph on board
the Hubble Space Telescope, of nuclear structures within four `warm'
Ultraluminous Infrared Galaxies (ULIRGs). We find an AGN in at least three, and
probably all four of our sample, hosted in a compact, optically luminous
`knot'. In three cases these knots were previously identified as a putative AGN
nucleus from multiband optical imaging. Three of the sample also harbor a
starburst in one or more knots, suggesting that the optically luminous knots
seen in local ULIRGs are the most likely sites of the dust-shrouded starburst
and AGN activity that power the infrared emission. The four AGN have a diverse
range of properties; two are classical narrow line AGN, one shows both broad
and narrow lines and evidence for lines of sight from the narrow through to the
broad line regions, and one is plausibly a FeLoBAL AGN. The probable presence
in one object of an FeLoBAL AGN, which are extremely rare in the QSO
population, supports the idea that LoBAL AGN may be youthful systems shrouded
in gas and dust rather than AGN viewed along a certain line of sight. The three
starbursts for which detailed constraints are possible show a smaller range in
properties; all three bursts are young with two having ages of ~4Myr and the
third having an age of 20Myr, suggesting that ULIRGs undergo several bursts of
star formation during their lifetimes. None of the starbursts show evidence for
Initial Mass Function slopes steeper than about 3.3. The metallicities of the
knots for which metallicities can be derived are all at least 1.5 times the
Solar value. The properties of one further starburst knot are consistent with
it being the forming core of an elliptical galaxy.
