I don't think anyone could adequately explain the exact pathogenetic mechanisms of these signs - many of which, the exact mechanisms remain unclear.
I found this particular article useful:
http://turner-white.com/pdf/hp_may00_endocard.pdf
And I have attempted to summarize the gist of that article below:
1. Roth's spot: Pathogenesis unclear
Severe potential mechanisms:
a. embolization of bacterial infiltrates from endocardium causing localized retinal abscesses
b. embolized bacterail infiltrates to retinal causing anoxia resulting in sudden increase in venous pressure, thus capillary rupture in the inner retinal layers
2. Osler's nodes Pathogenesis unclear
Few theories
1. Deposit of the septic microemboli from the endocardium
2. Nodes due to immunologically-mediated vasculitis caused by the circulating immune complexes.
3. Janeway lesion Pathogenesis unclear
Theories:
1. Necrotic microabscesses with an inflammatory infiltrate that involve the dermis but not the epidermis
2. Deposit of the septic microemboli from the endocardium
4. Splinter hemorrhage (this is a very non-specific sign - it can be due to many causes)
In IE, splinter hemorrhage is caused by the engorgement of the capillaries, resulting in hemorrhage. But what causes the engorgement and hemorrhage is not known
Some of the signs that I have seen in the most recent case of infective endocarditis:

Another picture of Janeway lesion:

A picture of the Osler node can be found in this website: http://dermnetnz.org/systemic/osler.html
Infective endocarditis needs Duke criteria for diagnosis. The full table for Duke's criteria can be found in many standard textbooks and it is not intended to be reproduced here but a simple mnemonics to remember their principles is like this:
BE FEVEER
(*BE - Bacterial Endocarditis)
Major:
B = blood culture +ve >2 times 12 hr part
E = Endocardial involvement from Echo
Minor:
F = Fever
E = Echo findings (not fulfilling a major)
V = Vascular findings
EE = Evidences from microbiological/immunology (2 evidences)
R = Risk factors/predisposing factors - drug abuse, valvular diseases
